100% agree with left handed drill bits. I've not had good luck with screw extractors.
I don't recall if OP's bolt can be run down and out the bottom of the tub or if it's captured by sheet metal. The way I'd approach removing this bolt without welding is
1. douse with penetrating oil, both sides of the nut if possible
2. file/grind the shank flat
3. center punch
4. apply heat. I typically use a micro torch or benzomatic torch kit. I'm super paranoid about a garage fire, so I don't own an oxy/acetylene set.
5. use right hand drill bits and cutting oil/lubricant to go through the bolt. Sometimes the heat from this process is enough to break the bolt free.
6. more penetrating oil
7. left hand drill bits to reverse the bolt out, or vice grips on the point to run the bolt down and out
8. chase threaded nut with lubricated tap