Aah! ian, next time you get in touch with Chris, let him know his videos are sport on! I watched his one on replacing the water pump in the alpha one drives. There are a lot of videos on Youtube regarding doing anything on boats, and Chris's are the only ones that are of any value IMO. They're so detailed - even down to the size of spanner/socket will be needed for each nut or bolt makes they super helpful, as you can make sure you have the tools you need before you turn up at the boat to realise you've left your xyz widget at home!
I actually watched that video last night, so had an idea what I was looking at before I started. Here's what I found.
1. First I tried to replicate the problem, and thankfully I could. With the engine not running, selecting reverse locked the prop from being spun by hand in the clockwise direction, le tthe prop rotate freely in both directions and, crucially, selecting forward did not lock the prop from being turned by hand in the anti-clockwise direction (which I would have expected). With forward selected, there was a slight clicky feeling when rotating the prop anti-clockwise, suggesting it was almost, but not quite catching/engaging with the dogs.
2. There was no evidence of anything looking bent, broken or in any way suspect around the shift plate.
3. I had taken no notes from the video, and had no reference with me, but I thought I'd have a fiddle anyway. I removed the shift cable from the shift plate. Sure enough, pushing it all the way to each end of its travel locked the prop in the appropriate direction when turned by hand. This therefore suggests that everything is working, it's just the adjustment is out for some reason (possibly a stretched cable)... unless I'm missing something?
4. I thought I'd have a fiddle with the barrel on the shift cable and see if I could improve things when it was fitted back to the shift plate. Sure enough, after a bit of trial and error, I had it so the prop locked correctly when shifted to both forward and reverse, and freed up completely when shifted out of both forward/reverse and into neutral.
5. Running the boat on the muffs, I confirmed that this remained true even under the engine's own steam. By pulsing into forward and reverse, everything seemed to work correctly. I also pressed the interrupt switch to ensure that was working - it was, so I presume this can now be discounted.
6. We had the boat dunked in the water, and with appropriate spring lines set up, tried again. It was tough to tell as there was a fair bit of current running but I'm about 90% sure it was working OK.
7. With the pontoon empty of other boats, we thought we'd try for real on the basis that docking shoudl be pretty low risk... even if we get stuck in gear or can't find gear at the right time etc. On the river, forward and reverse engaged perfectly, and again, I'm 90% certain that shifting into neutral (from either direction) was knocking out of gear. Sadly, with the current that last 10% of certainty was impossible to glean. In hindsight, I should have turned the boat perpendicular to the current and then tried! Oh well!

WoooHoooo! I've fixed it, I thought....
8. On docking, everything was fine - until I realised the boat was still pulling forward at tickover. It's weird, as it was only pulling forward very gently, and we were pojnting upstream (so with the current). We have just fitted a new 19" pitch Mercury Blackmax prop, so it could be that I'm just not used to the gentleness of the prop's force at tickover?
9. I tried to shift in and out again whilst tied to the pontoon. I seem to be able to get into forward/reverse with no drama at all. Getting out of reverse is fine too, but to get out of forward, I have to just nudge it into reverse slightly.
So, my fiddling did seem to improve things. To describe the adjustment on an arbitrary scale, it looks as if before I did anything we were at -5. I have adjusted towards 0, but perhaps gone slightly too far and am now at +1. SO...
1. Does it stand to reason that if I just back off my adjustment slightly, everything will be sorted and we'll reach the 0 point?
2. Have I adjusted the right thing, or have I improved things by adjusting the wrong part, meaning that the dogs won't be properly engaging now, or something?
3. Even if I have adjusted it all appropriately, and am on the right lines, I can't explain why it was out of adjustment (nothing has been intentionally changed since it it was working correctly). Therefore, assuming it is something like a stretched cable, is this likely to continue to stretch and forever need adjusting for... or even worse, just snap giving us zero control (most likely at a point where we will most likely need it)?
As it stands, I intend to completely reset everything in accordance with Chris's video. I expect (assuming it was originally set up correctly) that this will yield the same result as I described in my OP. Then, if necessary, i will repeat what I did today until I find the sweet spot where everything seems to work. If such a sweet spot cannot be found, does anybody have any idea what else needs to be investigated?
Many thanks in advance (again), and sorry for the super long post!