Denny, I think you'd be more likely to find someone with the "portable" setup, specifically because the process has little to do with "stability" and a lot to do with treating the whole assembly .... you've already found trying to deal with individual components in isolation didn't work
my first experience with truing was about 1965 with new tires on a '47 Buick .... same deal, tire shop had a hard time balancing them, had odd vibrations at certain speeds, took a recomendation to see an old mechanic who listened to my description and said I should true the front tires - I watched him do it and it worked perfectly .... a few years later when I got new tires on a '56 Chev sedan I had them done too, amazed at how out-of-round a brand new tire could be
as the other Bill says above, modern radial car tires don't seem to be so bad, but for the heavier truck tires and bias ply, I'd be inclined to think truing right away with speed related vibes - didn't know until this discussion the machines were still being made and used
Bill