When a tiedown is place in a nuetral position, IMO, it doesnt cause a problem.
I ride with mine fairly loose. It has a big noseband so it doesn't rub, I thread it through a ring on my breastcollar so it slides easily and he won't get his legs caught when we run around. I've never had a problem going down/up steep hills, through water, and pretty much any terrain.
I know a lot of people crank down their nosebands, but I don't. I have it just tight enough he can't take my teeth out again but long enough it doesn't constrict him at all. I use it when I run barrels too. He can run barrels without the tiedown, but it gives him something to lean on just in case.
Some horses don't like the tiedown so it completely depends on the horse. My other barrel mare can't stand them.
However, if you are completely dead-set against it, I also wouldn't try the combo. I find that most of them pretty much apply pressure in too many places (Nose, jaw, poll, etc)
I suppose this depends on what you buy, but I don't like them. I tried riding my gelding in one and he hated it. Especially on a green horse.
At this point I would do a LOT of groundwork. Maybe put him in the snaffle bit and work on suppling up, let the horse have his reins tied to the stirrups so there is give, and he learns to supple up on his own. I know a lot of horse owners don't do this, so do it by hand if you want. Teach him flexing by taking the reins in your own hands instead of the stirrups.
With the right amount of groundwork, you won't have a problem by the time you get in the saddle. Be prepared for that to take some time though.
Pssh.I didn't pick up the wrong lead
It's called a counter canter...
...A very advanced maneuver.