Cutting a slot in the screw using a thin disc in a dremel tool is a common method. It may be hard to do this without cutting into the emblem though. Harbor Freight sells some cheap "diamond grit" cutting discs that are really thin and would be good for the job.
Ah yes... those things can be a PITA. Seem to be made of case hardened peanut butter. That rusts.
If those screws are flat head, the head can be carefully drilled off, freeing the emblem from under the head but maybe leaving the threaded shank in the tank bracket.
What we're after is to free the emblem from under the head without enlarging the hole(s) in the emblem the screws pass through. Apply penetrant a few days prior to drilling.
Using a good, sharp cobaltleft-twist bit the same diameter as the crest diameter screw threads, slowly drill into the head. Because the head is already stripped into a dish, the dish is already centered on the screw's shank. Take your time! Run the drill very slowly. What we're after here is to drill just the head of the screw off of it's shank, to release the emblem out from under the head. Then, if the screw didn't unscrew from it's hole during drilling (likely), the emblem can be lifted off of the remains of the screw shank that's still in the tank bracket. Because we're using a left-twist bit, the screw will often unscrew from the tank bracket bracket early in the process. If not, apply penetrant to the stub & let soak for a few days. Vise grips clamped to the stub & rocking CW and CCW gently will likely free it. Heat can help, but only use a hair dryer on low or med to not damage paint. If it still won't free, it can be drilled the rest of the way out slowly & carefully using the next size smaller bit that matches the root diameter of the screw threads.
slmjim & Z1BEBE
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Is the tank going to be painted? If so, you could spray the screws w a penetrant & let it sit at least overnight. Liquid Wrench penetrating spray lubricant is a good one. In case you aren't going to do a repaint, I don't know if the LW harms paint. You could put automotive painters tape around the screw holes, something with low tack or stickiness so it doesn't pull off the paint; then add several layers of gorilla duct tape over the other tape for extra protection. Something else you could do is tape milk jug plastic to the tank w sm holes cut out for access to the screw heads. this should offer decent protection against the dremel or whatever tool you're using. you may have to cut slits in the plastic to allow for the curvature of the tank.