Ah, now if you weld and heat them up to its invariant point, or some other point near its liquidus line where you have a liquid-solid solution,
and then grip it with some vicegrips immediately before quenching it below 200 C to form your martensite, then you would be able to deform the nuts enough for the vicegrips to lock onto them and then extract them.
Of course you would have to take into account the fact that the vicegrips themselves will loose their heat treatment and they will become fused together with the nut you will need to grind off...
This approach seems possible, but the liquidus line should be in excess of 1,100 C and I don't know if many welders can achieve this or not, plus you have to keep it above that point while you are welding it and moving the vice grip around.
