Well, a TC IS a jackshaft basically.. so you have two already ..
and since there is no "one JS setup" but dozens, you can stack them as long as you have enough room on your kart.... (you didn't asked for it to make sense right

)
You should not just assume we know each and every model of each and every brand just by a number...
chances are we don't

So make it easy for us and SHOW what you got, not just tell
Anyways, I get it.. the kart you have runs it's jack shaft on the rear end of the engine mounting plate. (By luck I had the pdf in my kart folder)
And yes, a TC with an aluminium back plate will make it difficult to go past the edge of your mounting plate since it sits inboard quite a bit.
depending on the exact amounts and details you might be able to flip the JS-in sprocket and if it has a collar towards the mounting plate.. turn it around and you gained a couple of mm already.
But I guess that won't do..
next best thing I can think of is to to the opposite and move the engine inwards a good amount, then cut a slot in the mounting plate for the chain/sprocket ...
now you only need to move the JS-in sprocket "under" the mounting plate and you're set.
that means you may need a set of locking collars, you may even need a new jackshaft, if yours isn't keyed all the way for example...
I don't know, and I can't even tell for sure by the pdf (I'd say it's not *shrugs*)...
And that's where pictures come in handy
The more we can see, the more we can help
'sid
PS I'm not entirely sure.. but original stamped steel backplate might work.
the engine itself shouldn't make much difference.. surely not a centimeter ..