I know what you mean
The way I (mostly) dealt with this was by using Alex Kurland's 100 peck pigeon exercise, it's in her book Riding with the Clicker. When I started riding Jackson, we had to leave the field where he lived, and go to the field next door with knee high grass to ride. So the only strategy I could come up with was a version of this. I would mount up, and ask him to move off. Then I would click for one step, and treat. Click for two steps and treat, click for three steps and treat. Keep going until either I want to stop, or more likely horse dives for grass
I didn't do quite what she did at this point, I just reset the counter in my head and started again. In about two days, we were getting up to 50 steps without eating grass. At this point, I just stopped - he seemed to understand that riding was about riding rather than eating.
This was a couple of years ago, and now we ride out on a very nice Sustrans path, that's bordered with delicious herbs - especially that lovely stalky one with white flowers that smells lovely when the horse eats it - I think it's called Queen Anne's lace. He still understands that riding isn't the same as grazing, but can't resist the white flowers, so I usually tell him to eat the occasional one by just pointing and dropping the rein on that side
He's in the fatty paddock at the moment with tender feet as we have too much grass, so I'm like you and want to keep munching while out down to a minimum
Donald, I would love to know how far you walked? Jackson is overweight and needs exercise, and I wonder how much is the right amount. If he feels he doesn't want me to ride, I'll walk him in hand (usually doesn't want me to ride because he's tender footed but is happy to walk the track beside me and even trot a little). I go about three miles a day, either riding or in-hand but the weight's staying stubbornly on him and I wonder if we need to go further.