Well where I am now -
1. Pulled the fuel tank, dumped it completely empty, rinsed it with 'real' gas and then reinstalled and added 'real' gas (to eliminate water in the tank).
2. While I had the tank out and since the 'smoking' motor had a working pulse generator easy to get to, I replaced it while I was at it.
3. Replaced the fuel pump relay (up on the left side of the fairing stay - requires removing the upper left fairing).
Now she seems to be perking as she should - but I won't really know until I take her for a 300-400 mile shake down ride.
That will be a bit since I am off to the Mansfield RTE tomorrow.
Here's what is interesting -
I jumpered a switched hot to the fuel pump and put a meter on the fuel pump 'hot' while it was running to see if I saw anything.
You had to look close but several times the voltage dropped from 13-14+- volts to .6, stayed there and then came back.
So I changed the relay - which is what my original hunch was the problem.
This is not the first time I've run into this as I had one go bad on BlueBelle.
If it is fixed my money is on the fuel pump relay because as John said, I've never heard of a pulse generator going bad on a ST1100.