904 output shaft play

In process of doing my first 904 rehab.
Removing tailshaft and valvebody for inspection and clean. Decided for now. That’s all I want to address as I put 3k miles on it since last year and it’s in pretty good functioning condition with the exception of usual leak items and kickdown not engaging. I’ve correctly adjusted and tweaked it a thousand times to no avail. I found the governor has some wear on the 2 weights and was possibly sticking. Perhaps, that may have been my kickdown problem. But, still have to remove valvebody.
One of several small reasons why I’m choosing to do this. I initially had a mild hum for several months in driveline reaching 70 mph only. Addressed several things and nearly removed all driveline noise down to a bare minimum. Huge improvement. To go further, I looked at tailshaft bushing and bearing. I know without a doubt the remaining little hum is coming from the tail shaft as I can distinctly feel it between my buck seats. Plus, area of sound and I addressed everything else. Bushing did have small amount of wear. Bearing is fine.
After I removed every single item from the output shaft. I noticed a large amount of inward/outward play. Seems it moves roughly 3/8 of an inch. I know there’s a minimum and maximum amount of play your suppose to have by checking it properly.
My 2 questions are:
1. I don’t know if it’s deceiving that I’m witnessing this much play. Because, with all parts in place on the output shaft. It seems all of those parts would help hold the output shaft in a firmer position. With the c clips from the governor and bearing. I know the correct thing to do is to correctly check for the recommended amount of play and shim the interior end if need be. But, I’m trying to avoid that if my theory is correct on the other parts being installed. I have a ordinary cylinder head dial gauge. But, have no idea how I can rig it as I’ve seen on videos.
2. What wears that would cause just needing a shim on the interior end of the output shaft to correct it ?
3. Can someone post a picture of what these shims actually look like and where they can possibly be bought ? My understanding, is they are placed in between the c clip on the interior end of output shaft to take up slop.