The reason for the questions. It is possible that the HT leads and/or plug caps are bad. Yes, I know they were checked in an early post. Nevertheless ......
Briefly, the copper core inside the HT lead can rot. Verdigris. Copper Oxide. It is a crumbly, light green copper equivalent of rust. When it starts to go, it creates a gap in the conductivity. Sometimes the extra revs can give a bit of extra of High Voltage to allow the spark to jump the gap. Sometimes it can't. The plug cap and the HT cable separate and standard copper cored HT lead can be used as an emergency replacement. The cable is a push fit at the coil end and a screw fit at the plug end. The resistance of the plug cap without the cable should be 5k ohms. The coil itself needs to be earthed to the chassis. That earth can corrode.
Detail of this and of my experience with the 1300 are in the link below, but it is all relevant to the 1100. A Honda dealer told me it was old and Ok for its age. I subsequently fixed it.
Describing an issue with poor running on my ST1300. Symptoms were engine seemed to be running fine except with little low end power and a sensation of always riding on a rough surface. Revs had to be kept up in order to set off safely. It turned out to be HT leads and plug caps. Details...
www.st-owners.com
The second question about the ABS is a remote possibility, but it is very easy to check by pressing a switch. Let me explain. The Traction Control System works by cutting ignition to one or more cylinders (I think that is what I read) when it determines that the rear wheel is rotating faster than the front wheel. When it is starting to fail, the effect is intermittent, and can result is some pretty erratic behaviour - and if it cuts when accelerating hard, you can get pretty close and personal with the inside of the windscreen ! It will leave you struggling to get power riding along at 10 km/h in the gutter, and then suddenly spring into life.
The issue in this case is not with the ignition, but with the pulsar ring and / or sensors. But if you turn TCS off, then the bike rides normally. The TCS 'switch' is not a switch as such. When you turn on ignition, it is always active. To turn it off, you have to press the TCS switch after the dash lights have settled down and before you set off (I think). The operation of the switch can be verified by the Tcs lamp on the dash. Just press it and see if it makes a difference. If this sounds a little vague, its because I cannot remember exactly how and when it operates - its been a long time since I sold my 2000 ST1100AY, but I remember I had to do it at the start of each ride until my sensor failed completely. It is more likely to do it when travelling above 10km/h, but that doesn't mean odd signals can't make it happen at standstill. Just turn it off and see if it improves. If it doesn't then that eliminates this as a possibility.
Finally from me, the vacuum tubes that are capped and stick out slightly above each cylinder head - if they leak, can lead to a very poor running engine, difficult to coax up to speed - but can result in much backfiring and surging - or did when of mine became fully detached. I dont know how they would behave if one tube was just split or cracked - but I am not convinced about this as a suggestion in your case.
The right rear tube is normally attached to the fuel cut off valve to provide vacuum to turn the fuel on. I think you said that yours had been by-passed ?