20 years ago I looked at a map and chose the Steamboat area based on proximity to the WY border and distance from Denver, I figured it was a remote area and there would be less hunters if access from one side was closed.  Turns out the opposite was true!  The north end of the Zirkels (technically GMU 161) is popular with hunters.  It’s a very popular muzzy spot too as access is easy and there are plenty of ATV trails.  Not many hikers so if you see vehicles at the trailhead most will be hunters.
Steamboat has grown a lot in the last 20 years, it’s no longer a sleepy little ski town in the off season.  Any trailhead within an hour drive will be full of hikers, many of which were very curious of my traditional hunting gear last time I was there.  I would not let hikers deter me though, just be aware they will be on the trails and camped at some locations.  They can even offer intel on elk if you ask nice!  I keep going back as I know the area, which always seemed better than trying the learn a new one.  
Outfitters camps are permitted by the USFS so they know where they are, and I think they have to let the USFS know when they are occupied.  I’ve had good luck with other USFS offices asking for maps of these locations, which the outfitters hate but it’s public information.  The Steamboat office of the Routt NF is not as well organized but you can ask about an area of interest and they will tell you where the camps are.  They can also email you a list of the permitted outfitters too.  Most of the camps however are only occupied for muzzy and the rifle seasons, thus the concern from outfitters with having maps of their locations!  It would help if they would actually set their camps up a bit more than easy foot hiking distance from a road.  But there are plenty of guys willing to pay $1500 for a “wilderness” experience.  I also think outfitters put up camps to “claim” an area of public land as they don’t use all of them every year.
Steamboat Lake is also very popular, any nice weekend it will seem like Disney Land with all the traffic.  Most of the roadside campsites in the NF will be full of tourists and fishermen.  In addition this is also a popular area with grouse hunters so you’ll run into them even in the wilderness.  I ran into one guy who was 4 miles into the wilderness area with his dog.
If you are looking in the Seedhouse area the Greenville Mine road is passable but it’s rough (too rough for a trailer of any sorts so no horses).  There are logging roads not shown on the map that head east towards the areas mentioned above.  I’d call the USFS to ask on conditions as it sounds like it’s been a very wet year out there.
One other thing beside the early rifle deer (above 10K), there are now bighorn sheep up high in the Zirkels so you may run into the few hunters lucky enough to draw a tag.  And watch out for moose esp. driving at night.  And those big dumbass black angus.