Thanks all. I think I may have tracked down the culprit (fingers crossed).
I flushed the cooling system and changed the radiator fluid. Despite evidence of leakage from the water pump housing in the past, nothing is showing at the moment. I took Scarlett for a run (undressed - um Scarlett that is) and there were no issues but it wasn't a long run and it wasn't particularly warm at the time.
With too many things on the go at the moment I haven't had a chance to do much of anything for a month (and having a 2nd bike removes the urgency for repair). Anyway I've done a bit more digging and I'm pretty convinced this may be the issue (from:
https://whereisbobl.com/st1300/st1300-fuelpump.html ):
"As reliable as the Honda ST1300 is, there are a few known weaknesses. One of them is the Fuel Pump. Frequently the pump will fail somewhere around 100,000 miles, especially if you ride like Ironbutt riders tend to do, bringing the fuel level down very low, frequently. Pump does not like to be hot. Fortunately, it follows a graceful degradation failure. It will start to buck and lose power, possibly stalling. It will do this until you either let it cool down or fill it up with fuel. It may not do this again for tens of thousands of miles. Eventually it will repeat, and will no longer work correctly, even with a full tank. It is a good idea to replace it as soon as it screws up the first time.
I suspect that one thing that instigates the issue is letting a fairly empty tank get very hot, then taking off, which cools the vapor, creating a vacuum. I think this strains an already old fuel pump. I have no data to back this up, but it fits with my occurrence and descriptions that I have read from other riders."
The surging I experienced and then no problems once the bike has cooled down suggests it is similar to the article AND coincidentally, Scarlett has just kicked over 158,000 kilometres - pretty close to 100,000 miles.
I'm about to order a replacement pump and filter kit from the States and have a go at installation myself (unless I come to my senses and take the replacement parts to a service centre where someone who knows what they are doing and do the job - but where's the fun in that?). I'll keep you posted.