I,m not sure if you have any good sources for cheap tools there but using the edge of a strap wrench has worked for me
2 Piece Rubber Strap Wrench Set
you might be able to make something like that with a suitable size fan belt if you can find one cheap enough too.
Sometimes that whole squeeze too hard thing can help instead of hurt. Try threading a second filter into the front of the stuck one. It gives you a bigger gripping area and that squeeze deformation can make the second ring grip the first one (though being a circular polarizer is going to make any method more challenging). A lens hood or similar might also help rather than a second filter.