Skellyman, thanks for your post. Way to go on acquiring your T100! Having run into this issue before on older air-cooled carbed Bonnies from 2001 - 2008, I feel your pain. From my experience, even though you disassembled the carbs, and "cleaned" them, they are still most likely the source of your problem based on how long the bike sat. You'll most likely need to do a more thorough cleaning. If you still see any residue on any internal parts, your cleaning wasn't enough. And, yes, all the jets will need to be replaced.
I have had the best luck with tearing down the entire carb, and then soaking them in an ultrasonic cleaner before reassembly (see following video example)
Also, here's an example of a cleaner:
https://www.amazon.com/Industrial-L...pID=41HZ3gosGaL&preST=_SX342_QL70_&dpSrc=srch
One source of replacement parts is Sudco (sudco.com). You could try to look up the Keihin CVK 36 carb parts in their catalog, but I have had better luck just calling them and getting their help in determining the right jets and needles for my carbs (800-998-3529).
I also find it hard to believe that these carb parts are not available through a Triumph dealer. As far as I know, Triumph still provides all parts for all models since 2001. They may be temporarily out of stock, but I don't think any parts have been discontinued. If that was true, how would a dealer service these older models? That would be very bad for business. You could contact Triumph directly about that issue - see screenshot below.
Below is an exploded view diagram of your carb with the parts that I would replace highlighted.
In this process, you can also consider upgrading the performance of these Keihin CVK carbs by using aftermarket needles and jets. One kit that I have found to work well is the Dynojet Kit (see screenshot of dynojet.com). I also wrote a blog post about this on my blog site:
and a couple more related posts here:
Online parts sources that I have used also includes:
Basically, you are going to need to get these carbs and every tiny crevice completely clean and free of residue caused by the years of sitting. Every passageway needs to be sprayed with carb cleaner and forced open with compressed air, multiple times. Every rubber part that comes into contact with gas needs to be replaced. The floats heights need to be checked and adjusted if needed.
I hope this helps... and best of luck to you! Keep us posted on your progress.
Randy