Bunged Up Very Tiny Screw Head

That would be *can't* get any purchase...

I gave up on mine and just threw it out. It was an old Timex and looked well worn and not worth it.

My wife sometimes would take a watch to a jeweler that hardly charged much more than the price of a new battery.

I did the same taking the screws out of a iphone, this with a screwdriver bought for the job. I filed a tiny bit off the end of the screwdriver and out came the screw.

Any watch that uses slotted screws to hold the back on is likely not worth much more than a good battery. Go to the dollar store and buy a new one. Ten bucks - mabee 20 if you want to splurge - and you'll get one with the normal twist-off or pop-off back.

Watch? What's a watch? I'll watch what happens with this topic.

Yeah that was my first reaction too- but it's actually a pretty nice ladies all stainless with a Swiss quartz movement and good quality leather band. Wish they would have used better screws though.

More importantly, my wife says she still wants it!

I can't agree with that. The best watch I've ever owned (and still own) is a Casio atomic time waveceptor. It's 11 years old, sets itself nightly and automatically from radio signals, is solar powered with a 5 month reserve when fully charged, 4 alarms, world time and displays two time zones simultaneously, stop watch feature, count down feature, and has a stainless steel case and bracelet, luminous hands plus LED illuminated night light, and is waterproof to 300 feet. Oh, by the way, the back is held in place with 4 small screws. I've never needed to do anything to maintain it other than having the bracelet shortened when I first purchased it.

Slot heasd screws? The last Casio I had used reed&Prince IIRC. Might have had provisions to allow using a slot screwdriver, but who WOULD when the better option was provided.

They appear to be Frearson aka Reed&Prince slotted heads, but nonetheless, are a type of slotted screw heads. Your post denigrated "slotted screws" as opposed to "the normal twist-off or pop-off back." Reed&Prince heads are slotted. They neither twist-off nor pop-off.

A Reed and Prince is not a "slotted" screw, it is a crosspoint cruciform head (also known as a Frearson)

Virtually nothing of quality today is built with a "slotted" screws> About the only common use of slotted screws today is "stove bolts" and in some circles, wood screws (and even there, they are fast loosing ground to Philips and Robertson or even Pozi-Drive)

How about taking the screwdriver and applying a tiny drop of crazy glue or epoxy, then positioning it over the screw and letting it set up? You'd have to put some stuff around it to hold it vertical. It might hold enough so that it could then be turned out and if done carefully, I don't see much risk to trying.