Nearly my entire career has been spent with employers in two industries: medical device manufacturing, and military/government communication manufacturing. I am guessing here, but I strongly suspect that this has shielded me from the effects of manufacturing, and its associated testing, being moved offshore and/or to the contract manufacturer du jour. Device and system testing where everything is traceable, and out-of-box failures are intolerable, means more investment in what would otherwise just be an expense area to the industries where yield just needs to be "good enough". Also, meddev, mil, avionics, space etc. industries are slow to adopt change, so if it was "done in LabVIEW" fifteen years prior, it probably still is.
Only other industry that immediately comes to mind in this category would be some specialized instrumentation manufacturer (perhaps serving e.g., chem, biological, oil and gas) where the clever scientific/entrepreneurial types who brought that tech to market, are still in charge of things. Those folks perhaps want to see smart testing strategies and good instrumentation testing their instrumentation before it goes out the door.
That's the closest I can come to suggesting a strategy for your next move, Phillip. But I'll be darned if I can find much of anything that smells like that being offered up in the incessant LinkedIn emails I get. Heck, they can't even settle on what the term "test engineer" means.
Dave