Grid fitting midi recording to closer BPM

I've recorded a free-style midi keys, and would like to make a cleaner version. Since i vary pace a lot, this may be tricky. Is it possible to change the bmp without adjusting the midi notes at first, so i can apply a time correction once the BPM is close enough.

Besides this, any tips how i can ALSO move the sustain pedal when i move my notes across? Or is this a part of MPC where the support isn't mature yet?