I had a pronounced wobble under acceleration at about 38mph. With hands off the steering wheel the wheel moved probably +/- 10 degrees. It looked really bad, but the slightest touch of the hand stopped it. I figured it it was anything serious I'd have continued to feel it through the wheel, or when cornering, or braking, or something.
Once beyond 40mph it vanished.
I was frightened it was drive shafty. Or a power steering fault.
Anyhow, took it to the tyre place to see if I'd buckled a wheel or something (seemed like the least expensive place to start). They diagnosed un-even tyre wear owing to the tracking being out. When the guy pointed out the uneven wear it was blindingly obvious, but I couldn't see it until then.
Two new front tyres and 4 wheel alignment and the problem has gone. Time will tell if the uneven wear returns...
I've only done half your mileage. Perhaps you could swap your wheels front to back and see if anything changes?