Well, there I can help. I used to make this sort of thing in audio in my spare time at university, firstly The Adventures of Johnny Justice and later To the Castle of the Moon Men (neither of which you are expected to have heard, nor could you by now) but suffice it to say I can provide research materials aplenty.
At the moment your play is thematically most similar to Flash Gordon (my personal favourite of all the Gordons, Commissioner included) so I would recommend giving the episodes a listen, technically speaking they were a product of the 30s and contain far fewer tailored advertisements, but the first episode is worth it just for the scene where Flash and his girlfriend Dale escape Ming’s palace by swimming away. Flash does the swimming while dragging Dale by her hair. I desperately wish I was making that up.
For the feel of the ads, I would recommend you listen to an episode of Lux Radio Theatre, a phenomenally popular radio show that would get A-list actors to come on and recreate some of their best movies. The actors would always have to do a nauseatingly obvious ‘interview’ segment where they went on and on about how Lux dish-soap was the most important thing in their homes. Cecil B. DeMille was the show’s ‘host’, that’s how rich this show was.
Also, X-Minus One was an early fifties show that for me is the high-water mark of radio sci-fi, full of fear-mongering, nuclear Armageddon and Martians stealing your children for their invasion (that’s a real plot in one episode, by the way). Any episode will give you an excellent idea of the feel that sci-fi had in the 40s and 50s.
Last one, I swear. Journey Into Space was the BBC’s most well-known foray into radio sci-fi, a slightly darker, more technically minded show that had far fewer bangs and whizzes. It was massively well received at the time. Good for contrast, at least.
As to general tone and conventions of the time, most sci-fi of the 30’s, 40’s and 50’s that made it to the radio or big-screen were fundamentally about hubris. The mad scientist or evil alien race would stage their plan to destroy/rule the Earth with their devastating new-fangled technology, and only square-jawed down home American Will could stand in its way. Often the scientists on the side of ‘good’ were side characters, who were ultimately proven wrong by the folksy wisdom of the rugged protagonist. Destination Moon wasn’t about the scientists, who were smart but unable to get their rocket off the ground, it was about the bold, handsome entrepreneur who played fast and loose with the rules to get them there. Forbidden Planet was about the foolishness of combining the human mind with advanced technology, which only seems to bring ruin to all who find it. Pretty anti-progress in a lot of ways, something to think about.