A suggestion from Dad was to take the wiring off the back of the alternator, clean the contacts, and reconnect them. Grime/corrosion there might be a reason for the voltage drop I’m seeing at the battery side of the circuit when the alternator is charging the batteries.
I duly turned the engine starter battery switch to off, and started to take the positive lead off. The spanner joined the lug to the body of the alternator, and there was a bit of a spark. At this point, I turned off the house battery switch too (too late, of course). What’s weird is that I then tried to recreate the scenario where sparks appeared, and couldn’t. I can only conclude that there must have been a capacitor in the circuit somewhere.
Cleaned everything up, connected it all back up, and fired up the engine. Put the multimeter leads across the back of the alternator, and saw a very unpleasant sight of 17.5V being churned out by the alternator; either blown the diodes, or the IC regulator. The ProsplitR promptly detected that the voltage was far too high for a 12V system, and refused to pass the voltage to the batteries.
I called the local marina, and got a hammerhead berth – easier to get on to single-handed than going inside on the fingers. I figured it’d be a few days without an alternator, and with a CPAP and a fridge drawing down on the house battery (since the Delco is dead), there’s no way I’d get away without charging the batteries daily. I suspect that the second house battery is also in a bad state, but that’s a job for this weekend perhaps.
Front of the new alternator; different fan design 
Part number perhaps? 
Handily marked terminals by the guy from MB. The rest I covered with electrical tape.
Looked around online for a replacement for the Hitachi LR155-20B that was attached to the engine; none found in Ireland, but several in the UK – it’d probably be Monday before I could get it. Had a chat with Denis at the club (the boathouse captain), and he happened to have a spare one from our launches. Alas, it was the 35A edition, and I didn’t want to downsize the alternator (and faff around with taking it off again when I got the right capacity one). He suggested calling Myles Balfe in north Dublin, which I duly did, and after a bit of sticker shock, I had a brand new alternator in my hands this afternoon (local price was about 2.5x the UK price, but it was here, and it means I get off of the marina tonight, instead of paying for 4 or 5 days of marina, plus shipping of a heavy item – it all balances out in the end).
Old one came off easily enough, though I lost my 12mm socket down the back of the engine somewhere; can’t find it at all. Fitted the new alternator with a bit of hammering (on the bushing, but it failed to move), drilling (a washer to fit the top bolt, because the bushing wouldn’t move), adjusting the swing bracket (the new alternator is a bit larger than the old one), and a few choice mutterings and swears about the recalcitrance of certain bits of metal. A lump of wood acted as the brace to get the alternator in to place and tension the belt.
Getting the nut on to the bolt that the alternator pivots around 
Bracing the alternator so the belt would tension
Fired up the engine, and got 14.3 volts out the back of the alternator. That should do, though I may want to tune it a bit higher to get to adsorption stage.