This minivan has a condition that has gotten worse over the last year, rather dramatically recently. Between 30 & 40 mph the steering wheel wobbles back & forth, but the ride is still smooth. Lately, the condition starts by 20 mph. After 45 mph or so, the wheel gets steady again, and has no other issues. Less than 100K on the vehicle, and it is not the tires. Front end was checked out and no problems found. Smooths out when turning. I see there were TSBs on this vehicle regarding low speed wobble, but can’t access them. There was a TSB about Michelin tires; not sure if this was the same TSB.
I had a vibration when hitting bumps at low speed that turned out to be the rubber bushings being worn that wrap the front sway bar where it connects to chassis. The rubber pieces were $2 each, jacked up car, took of two nuts replaced and vibration is gone.
When they checked the front end, did they check for play in the 2 front halfshafts? This should be a very inexpensive check. If you need a rebuilt halfshaft (axle) it’s not gonna be an arm and a leg.
You say it is not the tires, but how have you ruled out a tire problem? The symptoms described are consistant with a bad tire, specifically an internal belt separating.