Cool idea. My first thought is that the general idea is doable, but it may work out better to modify your goal to something more achievable. If your goal statement is to paddle 50 different class V runs, you can easily get skunked as previously pointed out. Many of the runs you listed are elusive, may run only at peak, may not run due to dams etc, or only in a very short window.
If however you modified your goal statement to paddle 50 days of class V, bike 1000 miles while summiting 5 differernt mountain passes, or something of that sort, it would be more doable. A quick google map check of distances in a semi-random order from city to city of the main hubs you listed is about 1000 miles.
May 23 - Aug 5 gives you 75 days. If you boat 50 of them, that leaves you 25 days of biking all over the state, which seems reasonable. If its about 1000 miles, thats 40 miles a day over 25 days, which sounds doable.
If I were to try to morph this into a plan with more detail I would plan out a good bike route from town to town, try to be in each location at a relatively good time for the boating, and then boat whatever is running when you are there. If you have to hit a run two days in a row, so be it.
A couple of random thoughts...
1) Get a concrete schedule. Plan the bike route, the days of biking travel, and the days in each location. That way you can have some set times when folks in that area can hook up with you to paddle. If that one guy can't paddle all summer you will need boating partners. If you let folks know you will be in Crested Butte June 5-10, you will have a much better chance of hooking up with other folks. Hookup up with folks on the weekdays might get tough.
2) Get a crew. If you have a couple of core folks that can hang with you for a week or two, or the whole thing that would be great. Odds are you are going to be looking for folks to paddle with in each of the locations though. If you get at least one willing partner in each of the locations you head to, you will at least have shuttle and some home base help in each location.
3) Work the bike route. Check the passes, grades etc and figure out which bike path is the best. Also figure out timing on when stuff like independence pass opens, or other similar issues that might play a role. Get some help from one of the hordes of CO bikers who do stuff like ride the rockies or triple bypass (maybe you do that stuff?).
4) I'd ditch the bike trailer and hook up car support to transport gear from hub to hub. I know you think this is not manly enough for your trek, but its more practical. My gut feel is that hauling an extra 70+lbs of gear over 11,000 ft+ mountain passes will kick your ass. Also if folks tag along for the bike rides, you will be much slower than them. My take on the bike rides is plan out the different legs and try to get a couple of folks to hop on each leg with you. Might be better to have a couple extra folks with you just in case anyway.
5) Network on the buzz to gather some support. If you came up with a schedule for when you would be in each location, you could rally the buzzards in each area to go boating with you, give you a couch to crash on, or get on the next bike ride.
6) Enter the vertical challenge as part of your quest. The timing works out well and the VC suports AW and first descents. Might as well combine them.
My take on path is that you will get hosed on a couple of long rides no matter how you break it up. One potential path to get it kicked off would be...
1) Steamboat last week of may - steamboat runs early and is lower elevation, go there first.
2) HW colorado first week of June
3) Ark second week of june (only a couple runs here, maybe just a couple days)
4) CB central mountains second week of june into third week of june
5) Durango 3rd/4th week of june
6) Option A: Front Range Denver 4th wk june/1st wk July (big ride!)
Option B: stop off at hit something along the way. Crystal? / Roaring Fork?
7) Ft Collins 1st/2nd wk July. Gate should be opening on the big south, hoping JW and SH still runnable.
Back to crystal for north fork, crystal gorge etc. 2nd week of july.
9) Black Canyon 3rd week of July
I think that this is a somewhat reasonable timing, its hard to get everywhere at primo timing, but this is close. You want steamboat early. HW of CO to the ark, to CB to DGO is a reasonable path that hits things at a decent time in June. Big South is good July 4th, there will be something going on the front range en route. Hopefully the crystal will cooperate with flows on the way back. Last couple of years black canyon has had decent releases in July/Aug to make things runnable.
Anyway, thats my two cents. Sounds like a worthy adventure. I'm going to be taking off the 1st two weeks on June and I am hoping to be doing some CB / DGO boating. I'd be more than happy to help out with some gear transport or hook up for some of the runs. Good luck with your plan!