Engine is running! Time for brakes.
So would you cut them from the back?
Yep, from the threaded side where the flared/swaged shoulder is on the outside of the drum.
It's that flared part that destroys the hub if you try to press the studs out because it opens the hole so far that new studs won't fit any longer.
Once that shoulder is off and you press/knock the studs out new ones should go back in nicely without having to weld anything.
Pulling them in with the nuts and some washers like famous bob mentioned works great.
Once the wheel and lug nuts go back on nothing is going to move anyway and this will allow the removal of just the drum later on when needed, because the studs won't be swaged onto the drum any longer.
Also there is no safety issue about doing them this way, because the center of the hub centers the wheel anyway and as long as your studs don't spin when tightening you are good.
I realize people vary in how they do things sometimes, but this is the way I have always done them and never a problem afterwards.