We are not being rude or, if you did take it to be rude, we were not trying to be, and I'm sure everyone here that has posted cares for the well fair of all horses, yours, mine, theirs, etc. You posted a critique of yourself using a tie-down. You told us the reasoning for using the tie-down...and we are simply saying a tie-down should not be used for teaching to neckrein, and IMHO not at all. If a tie down is needed, then there are holes in the foundation of the horse, or the horse is emotional and scared...and the tie-down will do nothing but make the matter worse.
Gait wise, other than her being very on the forehand, I like her tempo and speed (besides when she was loping as you lunged her). I do not like seeing a slow western pleasure horse that looks almost broken because the gaits are so slow. Your mare has exactly the right speed that I like to see.
But I would like to add that all horses know what all the gaits are from stop, to back up, to w/t/c/g...it's when we get on their backs that makes them unsure of what to do. ;)