Ok 3 things :-
Actual
1) all that tiller is not helping when setting off
If you could build a stem that rotated up it would help you getting on and off and allow you to start off with it up thus reducing the tiller
2) your seat is very laid back , good for speed , again not helping when setting off , try using the vars and pulling yourself upright when setting off or at low speeds.
Possible
3) it is possible you have to much wheel flop ?
Simple test ? if you have an ordinary bike push it by just holding the back of the seat , it should just travel in a straight line and if it does veer off easily correctable WITHOUT touching the handle bars.
if the bike starts to turn and digs in with the front wheel rapidly swinging all the way into the frame AND not correctable just by holding the seat then you have a lot of wheel flop.
Compare with your build
Then practice practice then go out and practice some more ...
Paul
Your forks also seem to have no axle offset from the steering pivot datum line ?
You're right there is not enough room above for both, when I was testing having both above, felt really uncomfortable, it seemed like a good idea but didnt feel right, I thought just like you did, a 2 in one, but I saw online a small almost push button shifter, so I'm going to try that on the horizontal bar and move the break up to where the shifter is. If it all works/feels i can shorten the bottm of the bars some.There's something about the Tomahawk that just looks right. The bike is just so well proportioned. Those bars look much better though welding the more vertical parts in the middle looks to have left too little room to slide separate brakes and shifters on just above the grips. Maybe a combined brake and trigger shifter with just the one clamp will fit? Might I also suggest some welded on cable management to go with mounting the bottle cage. It'll get rid of a few extra cable ties currently doing the job. Any ideas on colour yet?