Insulating basement floor
 

My basement has a subfloor (5/8 plywood over 2X4 sleepers). I'd like
to insulate before I finish the floor, either laminate or carpet over
subfloor. Instead of tearing up the floor and perhaps ruining the
subfloor to install foamboard insulation between sleepers, is it
possible to drill holes in and shoot expanding foam to insulate?

I've recently renovated and redone the walls and I don't think
moisture will be an issue. I'm a bit concerned about air movement and
possibility of bowing floor and the mess I'll get into if I have to
remove the flor at any point.

Also, has anyone used the polystyrene that is 2" thick and strapped to
the floor, then the subfloor nails to the strapping. Would seem to
eliminate the cold gaps from the 2X4 sleepers.

Any suggestions?

Thanks,

Aaron