If you have or can borrow the proper LTM Lens to M-Mount camera you can test the lens on your M.
Take care with adapting any LTM collapsible to your M Camera... check for compatibility
Sounds like you have already tried this... keep in mind that there are different LTM to M-Mount cameras depending on the focal length of the lens (there are two different adapters that position the focus cam from different starting points).
You have two Barnacks so you may be able to isolate the focus (?) problem by testing with both.
If all of your lenses give similar focus problems, your camera may need a rangefinder adjustment... there are plenty of videos on UTube. I have not done it, but I understand it's a common issue and can be a DIY project depending on if you are technically inclined ;-).
One trick with the IIIf is to use the magnification window to the max (IIIf).
Your example photo is OOF across the entire range. I would be surprised if this was the case with all lenses. Choose your test subject that has objects at all distances. Does your rangefinder focus show the actual distance on the lens ring... you also might try to zone focus using f/8, f/11 etc. for example.
I am traveling on Sunday, but email me or post here and I will try to reply as quickly as possible.
Casey
Edit: how is your film back plate etc? and do you need a IIIf user manual and/or repair guide?
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