Can I get underneath a BGA mounted chip?
perhaps fron below with very thin drill bit and lots of care.

it's peobably easier to remove the chip using hot air, and then glue and solder the probe wires in (eg: use #40 enammeled magnet wire) then re-ball and re-solder the BGA. I find that 800 grit sandpaper works well to strip fine magnet wire.