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?

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