I understand your problem. Epxoy will be a temporary solution. If you can get some of it down between the bottom of utthe sink and the nut that night help. But since you can't loosen or tighten the nuts the chances of you getting much penetration between the faucet and the sink are low. Epoxy gobbed on the outside will be very temporary. The leverage and poor gluing surface are working against you.
There are tools for attempting to get the nut off. As others have mentioned a dremel would also work. You might go around every day for a few weeks and spray the nut area with wd40 or whatever your favorite spray is.
Those old porcelain cast iron sinks are pretty tough, I'd' even try a small chisel on your nut if nothing else worked.