I don't think I can completely isolate the wire feed system from ground with my set up. Would there be a way to block or buffer the errant incoming volt/amps from the tig torch to protect the motor controller??
First off, I'm gonna take an educated guess here... the component that's probably failing first, is your bridge rectifier... and it's probably burning up because it's operating at 24v, but getting hammered with HF energy in the KV range.
The HF arc starter is a massive noise generator. Tony's spot on, you gotta isolate it... but galvanically isolating only does PART of it... you've got lots of EMI rattling around that out will be very difficult to 'keep out' of your low-voltage drive electronics.
first off, replace your bridge rectifier with another version that has a much HIGHER PIV rating. Next, put snubbing on it- you'll need capacitors going between each of the legs... some ceramic disc capacitors... try starting around 0.01uf 1kv ceramic discs.
If your drive control system is very, very simple, it will have very few things sensitive to HF noise... in industrial control design, simplest is always best... but for all things, you'll need to make sure that the environment (which includes EMI both external and internal to your process) doesn't kill stuff...
...because wierd stuff happens. Nature doesn't care about what you want- she does what SHE wants.
You may find that the presence of HF causes the bearings in your drive mechanism to erode. It's basically an EDM process that occurs. Same thing happens to gearbox bearings in 3rd-rail and catenary-power railway equipment powered by variable frequency AC traction drives. Everyone understands that when an axle's contact brush goes bad, that the gearbox and bearings become a return current path, but the circulating AC of the traction inverter wreaks havoc on anything metallic in reach of it's field. Anything that does, becomes a haven of 'eddy currents'.
In a class once, I had some students that didn't understand what all the grounding was about, and couldn't figure out why so many of their systems had bearing and seal failures, blown circuit boards and sensors, so I got a paint pen and started drawing Kilroy, but writing "Eddy Lives Here" on gearboxes, truck frames, bolsters and nearby cabinets... They started maintaining the grounding better, and those weird issues went away...