Denny,
I had my 50 year old 16" wheels straightened prior to painting.
I had to find a specialty shop that does wheel repairs only. Most regular tire shops do not have the special tools required to straighten steel wheels.
They first spun each wheel vertically to see how much wobble was in each wheel. [I do not have a spec for run out..sorry ]....go for zero run out
The price varied for me from $5 to $40 depending on how much effort was required to straighten each wheel.
The wheels were then placed on a horizontal machine which spun the wheels slowly.
A large, hydraulic drill press looking device with adjustable fingers was positioned over the wheel.
The fingers were positioned between the outer ring and wheel centre plate...hydraulic pressure was applied to the slow spinning horizontal wheel and corrected the wobble.
The shop foreman told me "NEVER use heat to straighten a rim!"
The shop also walnut blasted, acid washed and painted my wheels.
Denny, I do not see why they could not straighten your rims with a tire mounted...unless there are some physical restrictions with the equipment used.
The sad thing for you, will be your paint job will be ruined during the process.
Another member of this board, Tiny, mentioned to find a frame shop....they may have the tools do do this work.
I found my specialty wheel repair place by asking my local body shop.
This was an additional cost for me, but I believe it is an area overlooked by most folks restoring their trucks.
Having straight wheels and running bias ply tires, I do not feel any front end shimmy or shakes.
Greg