The 10T TC will be fine, the rest
might be off though.
The general consens is in fact to get a gear ratio that will work with just a clutch, and then install a TC and be happy about the improved take off torque as well as uphill capabilities etc.
And, that is a very sensible way of doing it;
all good you can just proceed.
BUT:
You have an additional 2.43:1 ratio when you need it
provided by the TC;
soo, why not take a spoonfull of that extra and and use it to gain some more speed?
So personally, I'd say gear for 7.5 instead of 8.12;
and let the TC compensate for that (it will happily)
and not only have take off and hillclimbing capabilities improved, but gained almost 10% top speed as well
Without the exact weight and wheelsize of the kart
it's a pain to judge what'll work and what'll fail;
but basically if you're confident that 8.12:1 will work with a clutch, then I'm pretty sure 7.5:1 is still safe with a TC
(say 27 & 28 teeth instead of 28 & 29 for example to get 7.56:1)
'sid