How many miles on the car? It's 10 years old, original wheel bearings? Your front suspension components may be all new, is the rear as well? RTABs and other bushings? Push up front could be the result of something off in the rear too.
How much tread left on those front tires?
I'll share a story from a friend with an M3 with staggered wheel/tire setup. He replaced just the rears and had odd traction control behavior, even though the fronts had plenty of tread. True the tires were different brands/models, but I think the lesson learned was, any traction differences could effect "handling." He ended up getting new fronts of the same make/model as the new rears and the problem was resolved.
I run a square setup, but even when I didn't, I always replaced all four tires at the same time, even if I was using the same make/model tire.
Looking forward to hearing what you find out today.