Is there any way I can adjust the probability of the map generating specific biomes, short of making them the sole biome of the map?
No, Not without mods, but you can increase biome size to make them bigger, but idk if that helps.
Also, I literally was just on the Minecraft Reddit and someone said the exact same thing xD
If I had this power I would create a mostly-desert, mostly-mushroom island, mostly-ocean world, where you have to struggle to find anyplace with trees.
Yeah this resource pack is going to take a while...