the idea might corrupt your plan abit, - but away... how about a RC LIPO or LION Pack in paralell with the output.... super caps might be ok too.....
btw i love your ambition ... but its verging on insanity... a home made reliable transformerless? welder.
--- i want too say too, the best arc welding experience i have ever had, is with car batteries, - 24V... it so smooth like butter. so nice.
There's no insanity here just a lot of learning (through even more failing).
Also i'd rather not use batteries for welding, good batteries are expensive and bad batteries wouldn't work.
Anyways, i took the diode bridge apart only to find out that just one of the diodes had failed.
One of the diodes in the double diode shorted out throwing the magnetic field in my transformer out of balance and into saturation and blew the MOSFETs right out.
I did some calculations and assuming i get 4V out with 12V in i get a ratio of 1:3, this means that with 340V (rectified 230V) i would see around 113V.
Since it's a half bridge the diodes would see at least double making it 226V that's not including any current spikes so i should take 250V as my bare minimum.
Also digikey came in handy with their filters, with them i can find actual part numbers rather than write "80A diode switching" in the aliexpress search

Ps: cracked the failed diode apart to see what's inside. There are two silicon dies, each 2.5x2.5mm ( 2x6.25mm
2 in total) both with two bond wires each.
Two bond wires should be ok at 40 amps, the silicon die has a current density of 6.4A/mm
2, in comparison the TO-247AC (150EBU04) diodes were 4.16A/mm
2.