jazzrider, it’s real easy to “overthink” the whole “gaited horse thing.” Sit in the middle of the horse, balance yourself (a la Ft. Riley or Sally Swift), take your contact, and off you go!
Until you get into the show world (which is an evil place; there’s a real interesting thread in Off Course that will give a REAL education in the “don’t bees” of the TWH world) what the horse gives you with you balanced is what God/Bog/Nature/Whatever intended that horse to do. If the horse is moving easily and you can dismount after a few hours to a quiet horse with no unsoundnesses or pains then you’re “doin’ it right.” On the other hand if you’ve got a sore backed horse or a lame horse then you’ve got to find out if the problem is the rider (style, skill, tack selection, husbandry issue, etc.) or the horse (injury, conformation issue, temperment issue, etc.).
I always rode my Walkers in contact. Many who like a Western style don’t. I’ve always found that Walkers generally gait better with light contact riding. We’ve followed the old Cavalry system’ taught by the CavSchool at Ft. Riley before it’s demise, for many years. The military seat is balanced, centered, and the horse is ridden in contact. Not the contact of the dressage ring, but the light contact of the cross country horse. Your average Walker can do quite well with this style of riding. The soldier also rode one handed in the field (as might the cowboy) so he could use his weapons (usually pistol, saber, or lance) as might the cowboy might use his rope. There is no necessity to ride on a loose rein to have a hand free for other purposes.
A difference between the military seat and the Western seat is that the military seat also permitted taking of low jumps over logs, ditches, or other field obsticles while using a weapon. Taking jumps in a Western saddle can be done, but for a male it increases the chance that you’ll end up as a soprano in your local church choir!!! 
The roots of the Walker are as a working road horse. In the 19th Century roads could be pretty bad (particularly in the South) and a good traveling horse had to be smooth but also able to handle ruts, fallen logs, mud, swollen streams, etc. The Walker’s predecessors excelled at this and got bred. When the breed was established in the '30s the type was already common.
We’ll not talk about the tragedy of the modern show ring here. :no:
Use good “horse sense” with your Walker and you’ll do just fine. You sound like you’ve got sufficient background to sort out an “snags” you might run into. 
Good luck in the future!
G.