Thanks for sorting that out, Gadge.

Paul, your compression tests seemed to indicate that the problem is excessive compliance in your valve train. I began by suspecting that the problem was in the decompressor mechanism, but you've checked that out thoroughly, and there does not seem to be anything wrong with it. So, despite the Tecumseh manual's problem solving chart, which points strongly to the decompressor area, we need to find another source of the excess valve train compliance.

If I put the manual aside, and put experience with Intek engines aside, there are just five places excess compliance can arise:
1. Slack or worn camshaft bearings.
2. Damage to the tappet, especially its bottom surface.
3. Ill-fitting lower pushrod ball and socket.
4. Ill-fitting upper pushrod ball and socket.
5. Ill fitting or, more likely, cracked, exhaust valve rocker arm or rocker arm central pivot mounting.

1. I personally haven't seen an engine with slack camshaft bearings, but they are very easily checked, and I think this should be done.
2. You've looked at the bottom of the tappet, and there are still some mysteries to be resolved on how it became damaged, and whether that has any bearing on the compliance problem.
3 & 4. Problems in pushrod ball-joints are common on worn engines when the pushrods have been interchanged or replaced, but I have not seen them otherwise (except when there has been lubrication failure, of course, which can cause problems just as you are currently experiencing: the pushrods are usually hollow, and if the ball-joint seizes, the ball can break through into the inside of the rod below the socket. I've seen it on cars, though not on mower engines so far).
5. Rocker arm problems are not especially rare, though my experience of them cracking is on cars, which have very strong valve springs, and OHC Honda mower engines, which have design problems (especially with valve guides shifting upward so the rocker arm's movement is restricted). Problems with the central pivot mounting are of two kinds: spalling due to lubrication failure, and a multitude of problems when the mounting has been abused, for example by forcing it sideways.

So, can we have a look at the timing-gear-end camshaft bearing, and a report on whether it is noticeably slack please Paul? Then a check on the pushrod ends, and finally, a close look at the rocker arms and their pivots seems to be what we need. The rocker arms haven't been interchanged have they? Honda OHC engines are rather prone to cracking those arms - I have no experience with pushrod Tecumseh engines to indicate whether they have problems too.