These are good theories. As for Background 1, considering it gets so much extra stuff compared to the others, I suspect this might be everyone’s favorite dibs, Mordred.
Which… narrows down who Adrian can be… (≖_≖ )
EDIT: Because of the political bits and other theories bandied around, I’m on board with BG1 being Percival now. BG2 could possibly be Mordred instead.
The Lucid Dream Arthur route is sort of a misnomer, since you can play that part without being a lucid dreamer. But wow, this is an impressive guide! Thanks for compiling it!
Mordred and Gawain are both spoken about in third person during the dream flashback/conversation with Arthur, so it’s unlikely that they’re reincarnation options for the MC. I also don’t think we should dismiss the other variables seemingly tracking reincarnation. We know there are red herrings in the code, so we can’t assume that bg stands for background. The calculation might be based on the less obviously named variables, or even a sum of different variables (ex. ag1+bg1+cg1+dg1).
It was mentioned on the Patreon that different timelines are possible depending on the Camelot MC. Even if Gawain and Mordred are brought up in the dream, I don’t think it rules out other timelines existing where they are the MC.
MC’s past reincarnation hasn’t been set yet, so all the information revealed so far has to be true for all possible reincarnations.
Since there are choices where only “bg” shows up, it kinda feels like if there’s a red herring, it’s “bg.” 
I just scrolled back to 2023 and saw that the collected stats contained all those variables back then.
It’s true the MC won’t be locked into a past incarnation after the first dream sequence, but I think there’s still a chance for the MC to be either. Mordred, if not the MC, will most likely be someone’s past incantation.
I’d say both Mordred and Gawain are practically guaranteed to show up. They aren’t the MC since people in the flashback mention them in ways that make it clear they aren’t present, but the amount of times they’re brought up, combined with their prominent roles in the source material, makes it clear they’ll have roles to play in the present day (or they’re massive red herrings, I suppose).
If it wasn’t for the fact that Lust is the only vice that gets any variables, I’d theorize that the vices correspond to a sin committed in the previous, Camelot life. 
Maybe not for the MC, but for the other characters?
Pride - Lorelei?
Greed - MC (variable)
Wrath - MC (variable), Adrian (if Lancelot/Mordred)
Envy - Gwen?
Lust - MC (variable), Gwen?
Gluttony - Merlin?
Sloth - MC (variable), Percy (confirmed by Merlin) would track with Percival procrastinating/getting distracted while questing for the Grail
I don’t have a good enough read on either Cassandra or Broderick to try to place them yet.
What You Did
Interacted with Merlin: 0
Interacted with Adrian: 0
Interacted with Percy: 0
Trained Skills: 1
Worked on Phobia: 1
Stress Relief: 0
Internet Research: 0
Chores: 1
Pearls Sent: 0
Re-evaluation: 2
Magic: 7 Physical: 80 Mental: 12 Charisma: 12
Bold : 174 Sweet : 211 Sassy : -47 Optimist : 166
Silent : 11 Fear Level : 3 Phobia Level: 3
And with that, I am reasonably certain the max body is 87, as luck has a hypothetical maximum of +15 to any stat and I decided against training twice.
Merlin: Gluttony
Gwen: Lust/Gyneth or Envy/Guinevak (Gyneth, the Enchantress - If she’s not the Saboteaur/ Guinevak of Carmelide, if she is the Saboteaur). I think one of the 4 reincarnations is Guinevere (99,99999%), which further increases my suspicion that Gwen is the saboteur and the reincarnation of Guinevere’s envious sister.
Adrian: Greed (Lancelot or Mordred)
Lorelei: Pride (Gawain)
Percy: Sloth (He’s one of my top three suspects for being the saboteur, along with Gwen and Cassandra. I don’t know, but I have a feeling he’s not Percival, and one of the reincarnations for MC is Percival)
Broderick: Wrath (Kay)
Cassandra: Envy or Lust (Morgana?- If she’s not the saboteaur ). I strongly suspect she’s a Fae. Maybe not a reincarnation, but Morgan with an illusion spell. Perhaps she was the one who cast the obscurata spell.
I think this is the first time I’ve seen someone else theorize that Gwen is Guinevak! Guinevere is too good to pass up as a background for the MC, and if Gwen is Guinevak it would explain why there’s a content warning for incest and also why one of the ROs will NOT romance MCs with a certain background.
There’s also the fragrance Gwen is described with in a recent Tumblr ask… La Belle Dame Sans Merci, huh. That poem about a fairy seducing a knight and luring him to his doom? Sus…
The only detail giving me pause, is that Gwen appears to be the only traditionally femme-presenting RO, so if she’s the saboteur that means players are losing that option to romance.
I also like the idea of Cassandra being Morgan incognito, but would she really leave Arthur’s body in Avalon to go gallivanting around with the Harbingers? I guess the situation has become pretty dire (with two failed Circles already)
I’m 99% sure Guinevere is one of the 4 reincarnations. Gwen is pretending to be Guinevere. Gwen is obsessed with Arthur and pretends he’s talking to her when Arthur talks about Guinevere. Gwen fits the prophecy Arthur told: A gentle/broken lamb with the heart of a wolf. The saboteur isn’t Adrian or Merlin because Arthur said the saboteur is still coming; he says this after the Camelot dream to Lucid Dream!MC.
But one thing I noticed: In one of the Tumblr asks, the author said MC can currently train with someone who’s trying to kill them… Which means Percy is the saboteur or the author was referring to a future where all the ROs have appeared. Suspicious, very suspicious: Percy TRAITOR Longspear
If he’s the traitor, it will simultaneously be expected and unexpected. Since he’s almost exactly what he appears to be, which is sus in itself. Although, I personally don’t think it’s him. My money’s on Broderick.
If you look at the code when Adrian offers you drink, it mentions poison. Personally I don’t think he’s the traitor and that’s probably there to make you suspicious of him.
My guess is they might’ve meant the future when all the ROs are available. Otherwise it does mean the saboteur has to be one of the three currently on the RV which feels too obvious.
Poison is also there for Merlin’s snackies, so I think it’s a red herring.
Not only when he offers drinks to MC, but there’s also a poison variable when he cooks in the RV. But I also think it’s a red herring.
HELP ME. I DON’T KNOW HOW TO FORMAT A SPOILER 
Edit: Thank you 
Click on the plus sign next to the smiley face. There should be an option to blur spoilers.
I don’t know if it counts as a spoiler anymore since that part of the demo has been available for a while.
I don’t know if Bg is the variable that indicates MC’s reincarnation (because there are 16 variables; Ag1-4/Bg1-4/Cg1-4/Dg1-4), but if you’re right…
Bg1: Percival (It makes sense for the virgin knight and original bearer of the Grail to lose points for having lust as his sin or is a Serial Killer 
And those cuckoo options like pretending to have amnesia are very suspicious)
Bg2: No idea. But seems to be a knight.
Bg3: Guinevere (That’s the most obvious)
Bg4: Ninniane or Morgause.
The author said there will be two men and two women. There will also be two knights and two mages
One thing I noticed is that if you use magic to try to locate the enemy Fae, MC says MC is human… Which would rule out Ninniane since this dream wouldn’t block the player from any of the reincarnations… But maybe it’s a red herring and MC is just saying that because they don’t remember properly who they are?
I like your thoughts about Bg1 being Percival.
Since you’re sussy of Percy, do you have any personal theories about what character from the “enemies” categories of Merlin’s guide he might be? (Or even thoughts about what ally/neutral character would fit, if he’s not the saboteur but also not Percival)