Wait.. So this is where I've been going wrong then? I assumed that in the case of say, a cultivated princess and a cultivated majestic drone, using the soul frames would greatly improve my chances of them mutating into majestics? So that doesn't work then and if I want majestics then I'll have a better chance using soul frames on cultivateds and nobles?
Mutations are a process where breeding species
x with species
y gives you species
z. Species
z will never mutate to species
z because it already
is species
z.
As netmc points out, putting your majestic/cultivated hybrid princess (
z/
x) in with a noble drone (
y) would benefit somewhat from soul frames, but if the parents don't offer both
x and
y races then there's no chance of further mutation.
I had a pure drone but I lost when running it with a common princess + souls.

Maybe I should've kept the pure dili drone to one side until I had a <something> dili hybrid princess and then run it with that for a good chance of getting pure dilis?
Saving pure drones would be your best bet. Even if after five cycles you don't have the princess you want, if you've been putting aside pure drones, then you no longer need to mutate in order to get your princess.
Say you have a few pure diligent drones and you want a diligent princess. You put one of the drones in with a princess of any type, that princess is going to get the diligent trait as either active or inactive - this isn't a mutation, so you won't be using soul frames, this is just pure inheritance. You'll then have a diligent/hybrid princess.
You put that in with another of your diligent drones. Again, the resulting princess takes on the diligent trait from the next drone as either active or inactive - if its
other trait happens to be the diligent trait it
already had (50/50 chance of this), then you've now got a pure diligent princess. If not? Throw in the next pure diligent drone.
There's still some luck involved, so on average expect to require at least three or four pure drones to do it. You should be using this process to produce extra princesses before trying to mutate to a new species so's you don't lose the ones you currently have. Go scoop up a few more hives if you're running low on spares.