I was curious if I rewired the AC motors on both the squirrel cage fan and outdoor unit to DC, and hooked solar panels directly to with battery backup, would that be anymore efficient than converting to AC?
It really would not do you any good. The only power you'd save would be that which an inverter draws, and that's minimal. We live off grid and I can tell you that running a central a/c unit with solar will be exceptionally costly to setup and maintain. We use wind and solar and batteries and have over $25,000 in our system and I could not power a 220-v a/c unit.
no power is power, dc motors are dc motors and ac motors are ac motors, it takes the same amout of power to do the same amount of work, doesn't matter if ac or dc,just lower I squared R losses, they just like to use dc because it can be cheeper to vary the speed of the motor but you can't do that just by changing motors, maybe if you were in a place that had the sun shine 24 hours a day and a heck of a big bank of batteries it might be worth a try, they won't run long they draw more power than you think.. If you want to do it, get solar panels , batteries and an inverter and use the same motors you have. set up for automatic transfer, if you calculate it right it might be able to run for a little bit on the sun.
Don't AC and DC motors differ quite a bit in design? Is this even possible short of building a new motor?
