think you've pretty m uch answered your own question.

At a speed as slow as 60mm/s yeah infill squares that size are going to make a difference.

Never heard it called 'pillowing' before - but that's definitely down to the size and shape of the infill.

try using tringular infill.
At the same % infill it will drastically reduce the 'pillowing' as the areas being bridged change from small to medium, with tyhe square infill it's always bridging a large gap.