5010934R91 is the kit it contains the turbo / seal kit / studs / o-ring and
the bare re-man turbo part # 5010935R1. NAVISTAR only sells it as the kit.
So you have the correct turbo, it's just worn out. Not sure what the end play on the shaft should be but it should not be flopping.
NAVISTAR shows about 100 in their PDC. Most dealers should stock it, worst case it's a day or two out.
As a cash customer with a motor home you would be paying around $3800.00 at a NAVISTAR dealer.
You could call https://www.areadieselservice.com/
and see if they have this available as an aftermarket.