Infinity adjustment on Canon LTM lens

My interest in classic photography has been rewakened by the purchase of a Sony NEX-3 body and adapters for my various legacy lenses. I've been anxiously testing out my Canon LTM set, and finding that they generally perform well (meaning in part that the adapter is of the correct offset for inifinity on all the lenses). But I was surprised to learn that one of my "pride and joy" lenses, a Canon 35mm f/1.5 (clean black and chrome gem) has a recessed lens barrel. To make the lens actually focus on infinity with the infinity lock set, I have to unscrew the threads by about a millimeter! Put another way, when screwed all the way into place in the adapter, I have to set the focus on about 5 feet before infinity even comes into focus. I can only guess that a previous CLA might have threaded the helical thread at the wrong starting point, but I wonder if there isn't a way to rotate the lens cell forward with the rest of the focusing gear still in place, since the RF cam is evidently in the right place?

The lens flange has three screws close together. When I remove these, I can rotate the front cell freely, although this does not change the offset, and it just makes the aperture scale unaligned with the focusig scale. Can anyone suggest what I need to do to actually coax the lens cell itself more forward? I can check the live focus in the Sony, of course, which was something I was never able to verify about the lens when it was on a film body--I just thought the focuser was off. So if I can rotate the guts, I can tweak out the infinity focus and then lock it all back up. Seems easy, but how to do it?

Thanks for any suggestions. I've been away much, and hope to stay more in touch.
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Don