I live and hunt in Wyoming, and hunt with my cousin often, he has a 25" .270 Sherman, and built a 19" .270 Sherman for his wife, both supressed. I did load developement for both, and helped build both, as well as a 24" 7 mag with supressor. Yes, it's doable hunting out here, but we also go hunting in back country for mulies and elk, packing in 5+ miles at times, having to go over logs, under limbs, cross creeks, and ride horses. Our elk taken over the last 4 years have averaged over 700 yards where we hunt. Having used those three rifles, as well as my wife's 20"+brake 7 Max, my 24"+brake .338 Norma, and my 29"+brake .260 ai.....
I am building a 20" 30 nosler with a carbon barrel on an XLR folding magnesium Atom chassis to be run exclusively supressed. Getting a 215 to 2900 or so seems doable in a 20" 30 nosler, from other people's data I have seen, and will get me what I need for elk out to 1000+ where I hunt.
When it comes to performance, you will have a bunch of people talk about how a 20" big magnum cartridge will get the same performance as a standard bolt face short action cartridge, what I have found is the vast majority of these people have zero first hand experience, and they are simply wrong. A 20" .308 will not keep up with a 20" 300 wm, 300 prc, 30 nosler, 300 rum, etc......and I'm not sure why so many people are 100% set on trying to convince others it will when they haven't done it. Talk to the specialty pistol guys, they will set ya right when it comes to short barrels. Most other people are just guessing because most haven't done it.
As for your specific use, I would stray away from the 6.5, a 20" 6.5 prc won't exactly be an optimal 800 yard elk round. I would look at a 7mm as a minimum, and prefer a 30 cal. I am assuming you want to keep weight relatively light, and also assuming your can is a .30 cal Max, and will not be appropriate for a .338 anything. If heavier weight rifle and a .338 cal can were in the conversation that may change some things....
A 7 SAUM isn't a bad option, and is where I would start my search for an acceptable cartridge. A 7 WSM, 7 rem mag, 28 Nosler, 300 SAUM, WSM, Win Mag, 30 nosler, 300 PRC, 30 Sherman Mag, or possibly rum is what I would look at, depending on what your specific can is capable of managing. Determine what performance you want at your max range, then do your research and look for first hand load data, from multiple sources, on short barreled performance of a specific cartridge. I wanted an elk capable cartridge to over 1000 yards with the 20" tube, that put me on a 30 Nosler. For 800 yards, and since you already have the components for one, I would strongly consider another 300 WSM
Keep in mind, this is coming from a guy that has bang-flopped elk at 890 yards with a high lung, just below spine shot from a .260 Ackley, actually my .260 AI has taken 5 elk all between 703 and 940 yards, so I am fully aware that it is capable, and a 20" 6.5 PRC may be similar to my 29" .260 AI (156 @ 2940), so it would do it, but 7mm seem to put them down better, and 30 and .338 cals seem to step it up even more.