When I have to hit the breaks harder (not slamming them on, although it does it then too) at speed the car wants to rotate to the right/clockwise. I feel it pull that direction. Is that likely something with the booster or...?

Brother had an old Chevy truck that half of the master cylinder went on (I think) and that caused the front or rear brakes to quit working. That's kinda what this acts like, but it would be the right side working more than the left. Are these split right/left instead of front/back?

Guessing this is something I definitely want to get fixed before snow flies.

 

May be your lower control arm bushings that are shot on the right side.

Check that and if that checks out, then you can check out the caliper on the right side and make sure the pins are sticking

 

when is the last time you replaced your brake fluid? Should be replaced every 2-3 years so it does not rust the brake system from the inside out! If the caliper slider pins are sticking, dirty or need lubrication it can cause a similar issue to what you describe. Also if the fluid has rusted the brake system, it could be the pistons are not being able to push/retract smoothly in the caliper.

 

I just bought the car 2 months ago, so I don't know the history, doubt the fluid has been changed. The front drivers rotor isn't as clean as the other 3, so that leads me to think something is up with the pins.