disclaimer: the following tips are from my experiences as an auto mechanic, not as a knife tinkerer. they work on normal size nuts and bolts, but i have not tried them on the tiny hardware that knives are built with. use these tips at your own risk.
there are a number of things you can try before you completely destroy the head of the screw.
first stick the knife in the freezer until the handle and hardware are cold. this will ever so slightly shrink the hardware.
then my suggestion would be to (since you already damaged the screw) first get a hammer and give each screw head a good solid smack. this will ever so minutely deform the threads and hopefully give you a little relief of tension on the screw.
then, if you have it, the next thing is to try a slightly oversize torx bit and tap it into the rounded out hole. hopefully it grabs enough meat and you can then remove the screw.
if it rounds out again, try a chisel and cut a slot across the head of the screw and then try a flathead screwdriver. maybe an impact driver can help.
if that doesn't work, try a ez-out if you can find one that small.
if that doesn't work you'll have basically destroyed the head of the screw anyway and you'll have to drill the screws out and tap new holes for bigger screws.
good luck!