There is little question that a 17 Remington, or any variation, is a controversial chambering. Some swear by it and others swear at it.
You will loose some animals with a seventeen, and you will blow up some hides. If you limit your shots to perhaps 150 yards, on standing broadside coyotes, you should do okay. But, if you make a bad hit with a seventeen, you are going to rip some hide.....which makes it no different than anything else.
On those "no exit" 100 yard presentations, a 17 Remington is (indeed), impressive. But you will also see failures, sooner or later.
Anyway, when I think of Montana, and "med. distances" I suspect you have in mind (possibly) more like 300 yards? I know I do! There is no way to make a consistant 300 yard coyote rifle out of a seventeen.
(please, spare me the vivid, single event testimonials)
I think a 19/223 or maybe a Tac20 might come closer to your goal, if you seek minimal damage in a sub-caliber?
But. If it were me, I'd just get a 22-250 and select a suitable bullet for your application, that will (for sure) kill coyotes at 300 yards. No need to reinvent the wheel.
Yeah, maybe not as sexy, but has been getting the job done for many years. And, my goal is bang/flop. They should be lying right there when I walk out. No running fifty yards through the brush before they give it up.
BTW, for a several day hunt, with numerous opportunities every day, yes, you may be forced to clean a seventeen every 15/20 shots, to maintain accuracy.
Good luck with your choice, LB