I don’t think it will be possible to be the leading member of a large-scale federation in the post-Hegemonic west while also trying to prosecute a war of conquest and colonization in the east. The cost of a Halassurq crusade will be autonomy if not independence for much of the continent west of Erezza; they may send you their starving masses, but they won’t take your dictat in exchange.
As others have guessed, the sphericality of the world is a near universally known fact; there’s no reason for Theurges to try to hide it. But only the Dead have explored widely enough to have found the southern hemisphere’s continents, so far. No Theurge since Hera’s time has gone on a voyage of exploration, and the Halassurq magi are almost 100% focused on defending their western border and seas.
Fair enough.
Soil health is a 21st-century research priority in our world, after a couple centuries of scientific farming that treated soil as (in effect) an inert mixture that humans could adjust as needed for crop yield maximization. The core insights of the last few decades of soil ecology research – that soil health is inseparable from microbial and fungal ecosystems that we routinely destroy through overtillage and application of agricultural chemicals – weren’t discovered until after the widespread implementation of earlier research that was focused on intensive farming techniques.
Thanks to that earlier (brilliant, lives-saving) research, we have in our world, not just the gameworld, turned much of our farmland into deserts that would only grow hardy weeds if we didn’t annually dose them up with our version of alchemy. As in the gameworld, that process has made it possible to massively increase our population, while reducing our resilience thanks to increasing brittleness in our food production system. As in our world, there’s no simple answer – no ability to abruptly declare that everyone has to stop the old-modern way and switch over to practices that haven’t yet shown the capacity to feed us all.
Hera was in some ways the Haber of the gameworld. Discovering a literal Haber process now would be highly convenient for getting the MC out of their dilemma, but it would only be kicking the can a few generations down the road.
Anyway. Substantial Theurgic research has gone into understanding every step of how plants grow, so that Theurges can spur rapid growth in any plant (not just staple crops). That was the primary crop-related agenda during the golden age of Theurgic research, 100-150 years ago. They could have been researching how to make a wheat variety that permanently yielded twice as much grain, similar to the work they were doing with enhancing the properties of healing herbs, and releasing those improved varieties into general use.
But the Ennearchs in charge of the respective research programs took different approaches. The one whose Theurges were looking at healing herbs thought it was in the Hegemony’s best interest for everyone to be able to keep disease at a low ebb, preventing plagues with minimal need for hands-on Theurgic intervention. So they researched solutions that, once found, could be used by Jane P. Yeoman or Giorgios Slumdweller. (Their thinking on population control and mullow/shrub yam was similar, as I explained a couple years ago.)
The Ennearch in charge of crop production, by contrast, didn’t want her Theurges to find solutions that would free up landowners to massively boost their returns without ongoing dependency on the Thaumatarchy. Increased crop yields were undoubtedly needed to feed more Theurgy-fuel, but if landlords could just enjoy those yields without an annual need for the state mage corps, they might get more resistant to giving up their work force to the Harrower. So the researchers sought and found solutions that did require hands-on Theurgy, keeping the cornerstone of the economy under close state control. If the latter Ennearch had foreseen a future when over a third of the realm’s Theurges were engaged in agricultural promotion, she might have done it differently…or maybe not, seeing that as a later generation’s problem.
Even today, the confidence that they could, if needed, quickly research and disseminate a super-wheat is one of the things that keeps the Ennearchs from feeling that the food system should be a top-priority critical risk. (That’s also why, when push came to shove, their response to Cabel’s rebellion was “You’re trying to hold our food system hostage? Watch us shoot the hostage.”)
They might, however, be wrong. The golden age of research has faded as an ever-higher percentage of Theurges have to spend their time on maintaining the system (driving canal boats, ripening out-of-season crops, infrastructure upkeep, rolling Harrowers around) or war against Halassur, and fewer have been able to spend time in reflection or empirical study. As Phaedrx has found, keeping enough dedicated and high-level Theurges on hand for a serious research program isn’t easy even for the heir to the Thaumatarchy. The current Hegemony isn’t in a place to pull major new discoveries out of a hat.
Bloody, to start with; you’d be in direct competition with multiple other major factions who want it as their capital or a key part of their realm. Aveche is a highly desirable place, with rich agricultural land and mineral resources (including alchemical), spread around an inland sea that makes intra-regional transport vastly easier than comparably-sized regions like the Shayard Rim. It’s also a base from which you could easily cut off the flow of grain to eastern Karagon without cutting off your own trade (which could continue in the Sea of Aveche even if you made the River Fyrne and its great canals unnavigable).
You’d want to make sure no enemy got hold of both the cities of the strait, Aegre and Sescia, that allow admittance to your inland sea; that pinch point is vital for any Avezian statelet that wants to trade with the outside world. Ideally you’d want to hold the western coast of the Aveche Sea down to Aegre (currently part of Shayard) since those districts are also rich farmland but much less populated and urbanized than the Erreziano districts around the north and east coasts. If you wanted to practice a zero-Theurgy policy, you’d probably have a couple million hungry people in your territory…but noting the “bloody” part above, that gap might not last too long.
To be fair I’ve obscured the math a little, but here are the key passages from Cerlota that outline what I’ve been thinking:
A donation alone yields on average eight phials of blood, but that blood is thin on aether, and your diadem-cooking won’t add any aether to it, just lock in what’s already there. Like Cerlota says above, if you take donations ten times a year for fifty years, you’ll get 4,000 phials from someone over their lifetime. But because the brain and other tissues are so much more aether-rich, harrowing one person gives on average the equivalent of 8,160 phials (i.e. a whole body’s worth of blood, 80-ish phials, multiplied by “more than a hundred times the aetheric oncentration of blood alone”).
That’s way more concentrated than anyone needs for normal purposes; if you tried to use fresh-Harrowed “blood” to levitate yourself, you’d have absolutely massive wastage as the aether sublimes away faster than you’re burning it. So when a Harrower comes back from a harvest run (its tanks holding enough aetheric potential to flatten a small city) its contents get diluted down with appropriate solvents to a more reasonable consistency before being phial-bottled and sent out with Theurges like Chirex.
However, the Hegemony does also produce phials with a wide range of non-standard concentrations, and since military Theurges do sometimes set themselves to city-flattening and similar massive Changes, their bandoliers will have a lot of those “high-calorie” phials. Theurges on the border will generally go out armed with at minimum a thousand standard phials-worth of aether, more if they expect to be away from base for a while.
If you run out and you’re still in danger, there’s enough alchemical juice in your diadem that you could bleed yourself and the survivors of your squad and cook up maybe 100-200 phials – hopefully enough to get you back to a place with blood bandoliers and a new diadem.
Of course, you monster. 
No, the aether gap between kids and adults is in the brain, not the literal blood.