NYBo said: "I don’t get what reseating the tires in a different relative position on the rims would accomplish, other than ruining the balance. "
Wheels are not round. They have high spots and low spots - and if you can match the high spot of the tire with the low spot of the wheel, the assembly is more round. This process is called “match mounting”.
The same mountain bike said: "I searched in vain for any in formation on tire concentricity standards. Does anybody here have any info on this? Capriracer? … "
There are no specs in this area. Tire uniformity, wheel uniformity, roundness, balance, etc. are not regulated in any way. Nor should there be. The levels that cause problems not only vary from vehicle to vehicle, and driver to driver, but have changed dramatically from the past and will likely continue into the future.
And to add some more fuel to the fire: The OP didn’t tell us what he measured as an 1/8". It is pretty common for folks to measure the sidewall area in the lateral direction - and that is exactly the wrong area and wrong direction. Not only does the sidewall hardly contribute at all to “Out of Roundness” of the tread, it is the radial direction (Up and Down) that is the important direction.
Personally, I think the OP is going about this all wrong. If he is serious about getting rid of the vibration that he claims was there 4 years ago when the tires were new, he ought to have done it then, and he ought to have a Hunter GSP9700 RoadForce balancer tell him which tire(s?) are bad and by how much and what he can expect as an outcome (Yes, the GSP9700 can do that!)
Frankly, this sounds more like someone who is looking for a project to work on where he doesn’t have to spend money - rather than an annoying problem that needs to be fixed.