The advice about properly fitted screwdrivers is key if you're going to do anything with screws on doubles. A 60 Deluxe isn't a best gun by any means, but it's certainly nice enough that you don't want to mess up the screws.
Thanks again for all the help.
I tried the Brownell's specialty screwdriver bits and couldn't get enough purchase.
I looked at it carefully, weighed up my options, and
today did the unthinkable: got a extra-fine needle tip grinding bit and fit it to my dremel.
I masked the area around it with blue tape, and then took my ever-loving time using the tip, straight down, to clean up the slot and cut it deeper, so that the bits would be deep enough to get some bite- and quit rounding the existing slot.
After I was satisfied it was even and deep enough, I put the proper width Brownell's bit into an adapter and used the drillpress technique to gently and VERY FIRMLY apply pressure.
It broke free and unscrewed.
Interestingly enough, this is not a wood screw. It is a machine screw that fixes the trigger guard to the lower trigger plate at a point about 1/4" in front of the rear mounting screw.
I used Oxy-Pho creme to reblue it, and I'll be ok with the outcome.
It was on the bottom, and now just looks like a wide slotted screw, instead of a fine slotted screw.
Now I am figuring out how to disassemble the action to clean it.
Thanks again for all the tips you gave!