So I have basically never used a hydraulic wood splitter till a few months ago. Pre-inherited the inlaws yard machines 27 ton made by mtd. To me there seems to be an excessive amount of side play in the wedge. One side has screws for what seems like side play adjustment but even all they way in there is still an inch plus. How much play should their be? Just get longer bolts? Other than a pain to start when ita cold. Splitter does what it should.
Looks almost like you should have a wearing strip in the opening that would be adjusted with the bolts on the side like a piece of 1/2x1/2 stock looks that machine has some hours on it
In this parts diagram it lookes like there should be some square stock in there captured by the vertical bolts.
Not sure how much but that is the exact same splitter I had before I finally upgraded My wedge always had a fair amount of play that I often wondered about but it was never an issue. I do recall turning in the bolts on the side one time to tighten it up a little but it was still rather loose. I do know that my bolts in the side were not bottomed out like yours in the picture, I can remember seeing the threads on them ; 1/2-20 fine thread.
You can probably still get parts for it. Best bet is go to TSC but they might need model and SN. They can look it up on their computer. I've done that and yes, you have the right idea about the part you need.