i like experiments...

and can tell you what i think would happen-

if you put a synthetic over a carnauba, the synthetic is likely to just wipe off when you buff it...
you have the best chance by making sure that the carnauba is fully cured first- still a good chance that the synthetic wont bind, but at least some chance.

the only way to really know whether it did bind is to do half the car carnauba only and half with the synthetic over it. then inspect after- you can usually tell just by looking at the light reflections.
acid test is a wet car for me- you might be able to tell which part of the car has been waxed only and which has synthetic only when its wet.

worst case is that you waste the synthetic and your time...

 

i use caruba over synthetic myself.
i have a bottle of the pinnacle xmt swirl remover #3 and its a 12 oz bottle.
autogeek should say on the site how big the botle is near the price.

for deep pad cleaning, I use DP polishing pad rejuvenator. works great.

if you have any microfiber (which you should) use micro-restore detergent.
detailers domain and autogeek both have it.