First, did you try the 'ole soap trick? Get a bar of soap and roll the screw over the top so you get a little soap in the screw threads. It helps to prevent the screw from binding.

Second, by any chance, could your screwdriver be the issue? Screwdrivers wear over time. After a while they no longer properly fit new screws. They'll slip and bugger the screw heads. Along the same lines, cheap screwdrivers rarely fit right from the get go.

As someone that works with hand-tools for a living I rarely get more than a few years out of a set of philips screwdrivers before they need to be replaced. I consider them a "wear item" like rifle/pistol magazines. When my father would get frustrated with a bad screwdriver he used to take it over to the bench grinder and turn it into an ice pick. Unfortunately this led to axle grease flavored ice being the norm out in the shop.