Removing Stripped BB Retainers
 

Nope, but I'd try a heat gun (begin on a low setting to save the paint) and try prying the plastic out once softened. Good luck!

Go ahead and try the drive side first. Remember it's reverse threaded. I always find a way to bolt the BB tool down when I start to keep it from hopping the splines. After the pressure is off, the NDS might spin free. Even if it was installed without grease I don't think there's any way it can fuse to the shell, can it?

No experience with these, but lots with plenty of other stripped BB's and many other things. If its plastic I would have already carefully ground out a small section so I could break it out without damaging the threads but being fully prepared to restore them as they will probably need that anyway. I have an air dremel like tool that with a burr can get in to very tight spots. Self made custom rethreader tools have never failed to resolve the aftermath.

This once again brings up the BB conundrum of not removing it for service until something goes wrong. This is a perfect example of that. Now you have more of a problem than you want. IMHO BB's should be completely disassembled whenever servicing any part of them. This especially includes driveside cup removal for thread service to help avoid problems like this later. I know many disagree on this and that is fine, I will always do it as a proper service so there are less of these posts.;)

most cartridge cups have a 1/8"or so lip on the DS that you can often get a pipe wrench on.

Is that the bike that had the really cool Ritchie crankset on an ISIS drive BB?

Wow, having cut, drilled, ground, and sawed frozen spindle cups out of BB shells, your challenge seems rather tame to me. What I would do is heat up a thin crappy (don't use your good one) screw driver with a torch and then push it into the plastic. It should melt right in. If you think you have good purchase with it you could try tapping it tangentially with a mallet to break the threads free. If it won't come free, just use the hot screwdriver to melt completely through the plastic retainer in a few places. Then with a bit of strategic chiselling, the thing should come right out.

Wow, never had to cut, drill, grind, saw or otherwise butcher any cups, ever, which is key when the offender is odd, rare or otherwise should be saved if possible which imho is always. With my method they always come out, never damaged a frame, cup, tool or otherwise. Only been doing this for about 50yrs so maybe I haven't seen it all. ;)

The hot screwdriver sounds like a pretty good idea.

I accepted a early 90s Bianchi frame with a broken spindle as a partial trade for another vintage frame. The owner had taken it to a number of shops who declined on the work, declaring the frame toast. Like you, I had never met a BB that I couldn't remove with a little patience and intelligently applied force and since the frame was otherwise really nice, I was happy for the trade ... had I only known that I was up for over 10 hours of work to get the thing out. I started with penetrant, gentle heat, and sufficient time to let it soak in. No go. Tried a pipe wrench on the exposed NDS cup threads. No go. Put the DS cup in a big bench vise and used the frame for leverage. No go. I finally decided that the only way that it was going to come out is if I cut radial reliefs through the cup almost down to the shell threads. The problem was that the spindle needed to come out first. I drilled a circle of holes around the spindle on my drill press and then used a dremel tool to cut the metal between the holes, which allowed the spindle to come out. Then it was just a bunch of grunt work cutting radial reliefs in the shell, first with a dremel and then with a hacksaw blade as I got close to the shell threads. I have to say that the cups are hardened especially around the bearing surface so the going was slow. After making the radial cuts I was able to use a punch to collapse the cups slightly inward allowing them to be removed without damaging the shell.

Although I was ready to give up a few times, I am glad that I persevered. That frame is now one of my favorite bikes (650B conversion). Since then, I have gotten 2 other free frames with rust welded BBs. Neither of them responded to 2 hours of work (now my guideline for this sort of thing) so they went for scrap. The lessen in all of this is to use anti-seize or grease for any BB installation. I am not sure that removing the BB every few years would be necessary if you grease the threads, but it's easy enough to do.

To OP: sorry for the slight diversion. Glad you found success.

A shot of penetrating oil. Wait 30 minutes.
Remove bb from drive side.
Vise grip on retainer "lip".
Cut out with hacksaw blade or Dremel too.

...stop right now, take a break, have some coffee, and relax. Then whenever you restart, apply some 50/50 acetone/ATF mix penetrant to the drive side threading, give it 15 minutes to wick in, reapply and attatch your cup removal tool firmly to that side using a bolt threaded the same as a crank bolt, but long enough to reach out past the removal tool, with a fender washer outside of that tool so you can firm it up.

Use a Crescent or other wrench on the tool, and strike it firmly a couple of times with a dead blow or other hammer to break any corrosive bond in the threading with impact. Once you have the drive side and the BB sealed unit out, you'll have better access to the plastic cup you're having trouble with, and maybe you can just cut it in a couple of spots and break it out from there.

I love a happy ending!

Honestly there is no reason to remove the NDS first on a standard UN type BB. It isn't a "lock ring" per se, more of a centering and stabilizing ring that doesn't attach to the DS and cartridge.
I normally do try it first as then the tool can be bolted into the axle to hold it in place, but not required. On a plastic cup NDS removing the DS first allows destructive removal of NDS much easier.