Any ideas on how to remedy this?
Remove the galled nut-bolt and replace with new ones.
When I need to weld a nut, I usually try to coat the mating bolt with either a good coating of NeverSieze or Anti-Spatter and thread it into the nut BEFORE welding. Helps to keep the nut's threads clean better than just sticking a dowel in the hole AND it helps to reduce the inevitable thread distortion on the nut caused by welding (you can still booger up the nut with all of the heat and solidification contraction when welding).
And a Grade 8 fastener IS certainly a heat treated (and thus heat treatable) medium carbon steel material (per the spec that applies to Grade 8 fasteners).
Of course, your coarse threads should have been 'cleaned' up if you ran a tap through the nut after welding. If the threads were not put back into the size spec after running the tap through, then the tap 'failed' in some way (possibly worn out).
And if I'm welding a nut/bolt, I usually just use a Grade 5 and not a Grade 8 as the welding heat is going to modify/change the nut/bolt mechanical properties after welding no matter what. So why use a harder/stronger and more expensive Grade 8 when it won't usually be a Grade 8 after welding anyway?
You DID remove the usual yellow zinc coating from the Grade 8 nut before welding, right? Zinc in the weld puddle is not what you want to have for a 'good' weld.
And "spot weld"? Although it kind of is possible to "spot weld" a nut to a plate, most of the time you are putting some "tack welds" or a weld bead around the periphery of the nut to weld it to the plate.