If I'm not mistaken I believe those "position changes" messages generally point to guys who aren't good enough to play the position you have them listed at..
So It will tell you your C with a 5/15 range/glove should be changed to DH, or that your RF prospect with a 50/50 arm should be moved to LF,

Maybe it is just that I've never had any SS types playing 1B, and regardless of where I actually play them I generally leave them listed as a SS, but I can't recall ever getting one telling me to change a 3B to a SS or whatever.

I don't think 'the game' thinks in ways like that.  Even playing a future SS at DH, his defensive ratings will climb the same way they would if playing SS the whole time.  And being at DH does not decrease the chance or severity of injury.  I know there are many other ideas to the contrary, but playing time is playing time, whether a guy is sitting on the bench as the DH (but getting ABs) or playing in the field (and getting ABs).

If I had to guess on what the engine uses to assume playing time, it is ABs.  Not where or how often you are in the field.

In my experience SS, C, and CF tire faster than 1B, LF, and certainly DH.  If all of those players are 80 durability the C, SS, and CF go below 100 first.  This tells me that the playing time being used by the engine is at least partially based on positioning.  Harder position to field uses more durability to play.  Unless of course I am missing some other variable that I am not taking into account.

Part of the equation on improvement in this game is based on "playing time" not position played I will grant you that.  I just think that by playing a more difficult position you can get more credit for having "playing time" if you play SS rather than 1B or DH.  Just as an example I will say the same player with 80 Dur might be able to play 80 games in a row at CF until he goes below 100%.  If you put him at DH he might be able to play 100 games in a row before he goes below 100%.  In those 80 games the player improved just as much as he would have by playing 100 games at DH. 

The rub is most don't play prospects much below 100% for fear of injury.  IF you played a guy at SS for 140 games he would see more improvement than if you played him at DH for 140 games.  However in order to play a prospect with a Dur of 60 at SS for 140 games they would likely be down to about 50% by seasons end and the chance for injury (negating the extra progress) would be very large.  

I jinxed myself, brand new 26 million dollar SS prospect already hurt

https://www.whatifsports.com/HBD/Pages/Popups/PlayerProfile.aspx?pid=5365600

It's 12 days due to my high medical, so my question is do I put him on the 60 day DL? Or should I wait it out. Once on the 60 day DL, I'm supposed to wait the full 60 days to get him back all the way up right?

The only category he lost ratings in is AS, and therefore that's the only rating he will gain due to injury recovery.  7 day DL with rapid return will work better here.

I do the opposite, don't let my ML guys get below 100, but let my prospects play all season no matter where their fatigue gets to.  Never had one suffer a significant injury because of it.