you’d need a battery tab welder at least. You can get pretty decent high drain 18650s for ~$2/ cell, so if you have 4 packs to do you could easily do so for $200 or so, depending on which tab welder you get. Don’t bother trying to solder the cells - not from a damage perspective, but from having to fit the cells back in the case. There’s not much spare space in there!
As for disconnecting the BMS board, that’s a tricky one. I’ve recovered bricked batteries by charging individual banks, but the only time I’ve rebuilt a battery (large 40 cell ebike battery) and disconnected the BMS, it didn’t work ($800 mistake right there). I do have a lawn mower battery I’d like to build using a spare board, but I’ll wire in a “dummy” pack first to make sure the BMS lights up. One way around this when rebuilding packs is to hotwire in a “dummy” pack of the correct voltage, remove the old cells, add new cells and then remove the “dummy” pack. Not done this myself, but the theory is sound (make sure both old pack and “dummy” pack are at the same voltage) and I’ll be doing this the next time my ebike battery needs rebuilding.
Oh, and for high current draw applications, you can use 10mm x 0.1mm pure nickel strips and sandwich a layer of 0.1mm copper sheet between the nickel strip and the cell. The tab welder will weld straight through and make a solid connection between all three.