Hi, I think the problem is indeed within the shutter release shaft. Either the spring has snapped and is restricting the shaft movement or something has come loose and got stuck along side. I've removed the base plate and I can push the shaft back up into the firing position, but once depressed it stays down. Also it seems stiff to move, the first day I had it everything worked great so it is a little frustrating.
From the links you posted me it seems that I would have to remove the leatherette to get to the lens mount screws, once the lens is off it should be fairly clear what the issue is.
I would like to try to fix it myself, I love older cameras and the skill would be extremely useful - but as you rightly pointed out the Lynx isn't the kind of RF to practice on. It took me a fair time to find one which was in good condition and that was a reasonable price I would hate to ruin it.
Also the finder spot isn't the greatest, I'm not sure if all Lynx 14's suffer from a dull finder but I have a electro 35 GS which is lovely and bright and i recently picked up a Konica auto S2 which has possibly the brightest finder I've ever seen, so once I take off the top plate maybe the mirror will need replacing - That I imagine will be another post!