Jensen didn't end up sending it off to check balancing, but it didn't need it. The turbo is running fine now, no leaking, no boost issues.
If you were to send it off though, look for a local Diesel overhaul shop that has a turbo test-stand. Otherwise, send it off somewhere like Gpopshop. If you do a google search for turbo testing, you'll see there are plenty of shops that can test your turbocharger for a nominal fee. If you send them a new wheel they can balance it for you for an additional charge.
Shaft play only affects the "factory" balance if either wheel comes into contact with the housing and is damaged. When the bearing seals go out, the bearings typically aren't completely damaged. In some rare cases where you run the turbo KNOWING it's blown for hundreds of miles though, you'll do damage to the bearings that will cause the shaft to wobble and damage both the turbine and compressor wheel.