An update. "Walkinthewalk" here on the forum (Judy) PM'd me to see how I was doing. SO kind! I went to reply to her, but couldn't because I've only done 2 posts here, and one needs 5 in order to PM. So, hopefully Judy will see this here.
After reading the responses above mine (page 1 of this thread) I went back to that book. It helped me to decide to continue to work with my current endurance saddle rather than spend money on a new Land Fox cutback, and gave me a general direction to go re: aids, and general seat position. But I still wasn't getting a feel for how to signal her gait. When I asked her for any kind of speed, she'd jog or trot, and it's a rough one!
THEN, by God's grace, a friend who has YEARS of experience in English seats and knows the rudiments about gaiting invited me to go on a rail trail with her, about an hour away, in her trailer. We loaded up and went. I attempted to get Grace into her gate, and my friend said, "You're leaning forward when you ask her, and you're not collecting her enough." I wasn't supporting her enough with my hands, and I was leaning forward (insecure, I think, as someone above said, after years of being off). My friend demonstrated on her horse: collecting the reigns, she urged her horse into the bit, and asked him to trot. With that one piece of input, all fell into place, and I was all set. I sat almost in a chair seat, collected up her mouth, and asked her. She went right into a lovely easy gait: push button!
I really should have known, because as a child, my cardinal flaw when riding saddleseat was to lean forward too much when I asked for the canter (in anticipation of the jump she'd make, I guess). My instructor always had to remind me to sit back and upright on my saddlebred when signalling the canter. I think because I had no idea of the correct signal to get her into the gate, my insecurities had me doing what I'd always done wrong, and thus confusing Grace. So, here I am at 55 relearning that same lesson!
I must say that between the lovely, easy gait and the endurance-style Sycamore Creek saddle that I have (which is designed for easy-gaited horses and leaves her shoulders free to do all that they should), I could probably sit that gait for hours at a time.
I now perfectly understand why this four-beat gate was developed and prized among circuit rider preachers and mailmen on horseback, etc., back in the day!
Now, my next thing is that there seem to be more than one type of easy gaits... something like, maybe, the difference between an amble and a fox trot and a rack??? That kind of thing (going on only what I've read in my book).
I can feel this on Grace. It's like a difference in diagonals when doing a standard trot on non-gaited horses; sometimes Grace seems to pick up one kind of four-beat gait, and then on another stretch of the trail, it's still four-beat but it feels different. So, that's my next challenge: figuring out finer points of gaits.
But I'm VASTLY encouraged that I now have the aids to get her into one of the easy gaits. I don't feel like I'm ruining or frustrating her anymore. Now I feel that I can "just ride" and also (I agree) step down her bit, and also just enjoy hacking on trails (she loves to go). I can't wait to go again! OH MY, those gaits are nice!