Brakes are fine. 'new tires on rear' is a general rule for the ages on cars.
It's physics, if your front wheels slip a little, u get a little squeal and understeer, if your rear tires slip but your fronts hold you can spin out very easily.
Decided to do a little inspection today after doing a few things that clued me in to check my timing belt.
Removed Ignition, and tested vacuum while cranking engine Got between 1 and 2" Hg, and it was bouncing between the two. (not steady)
Noticed excessive? air being pulled through PCV valve...
I've got this on my to-do list.
Local Internet enabled dealer quoted about $115 for cooler, its the only option available (previous style discontinued....)
Get a cheap OBD reader and watch the PID's for fuel trim.
if the fuel trims are way high, it could indicate vaccum/air leak on the intake.
If its running super lean, you could have leaking injectors.
No code stalls/failure to start are usually something wrong with the A/F ratio. Could be IAC...
Check the transmission cable on the throttle body.
I think it adjusts the pressure/slip for shifts. Mine was too tight which resulted in some weirdness in shifting. Setting it back proper made everything run better. Since you just worked on that part of the engine, could be something to check.
I'd definitely recommend it. Leaking axle seals cause a mess, and you are in the mileage range that it could go out. Even if they might last a while longer, they are older so just the act of pulling out the axles might cause them to go bad sooner.
Be careful just swapping the fronts if you will have newer tires there! you always want better traction in the rears or you can spin out very easily!
I swapped the fronts temporarily like your plan and totally lost control on an on-ramp. I got very luck as no one was around and there was tons...