'Liquid Wrench', (or 'Kroil' if you have it), will penetrate a lot better.

An electric soldering iron, held on the screw-head, will give you a manageable, local, 'heat source'.

You are probably 'fighting' old hardened grease, swollen wood fibers, and some deformation of the screw-head.

A sharp awl or icepick point neatly cleans the bottom corners of the screwdriver slots, allowing a better/deeper screwdriver fit.

Some screw-head slots are slightly 'dished', preventing a square screwdriver blade-tip from evenly touching bottom.

Radius the blade tip to match.