I just asked about similar (maybe slightly shorter) hikes in Colorado, for next summer. I'm also thinking late-July/early-August. My buddies and I are trying to research hikes all over the state, so that when they fly in we can go where the weather is best...
The CDT in the South San Juan Wilderness. A bit short- only 52 miles but the guidebook sez 5-7 days. But...
There are several ways to traverse the Weminuche Wilderness. Wolf Pass Trailhead to Ivy Creek Trailhead. Fern Creek Trailhead to West Fork Trailhead (has hot springs near the southern trailhead, but they tend to be crowded). These will all be a bit shorter than you want, but you can connect any of these trailheads to the CDT, in either direction. That would be one way to lengthen the South San Juan CDT hike.
Steve recommended the CDT in the Weminuche Wilderness- that's 85 miles. But just imagine connecting that with the 52 miles in the South San Juan Wilderness! I think, with the bit of National Forest that you have to cross, that it comes to a hair over 150 miles...
Sorry. Fantasizing a bit.
The last 75 miles of the Colorado Trail, Molas Pass to Durango. Accessing the trail north of that is difficult without a 4WD, until you are well north of Coney Mountain, but that would STILL be within in your requested distance.
This one is a bit short, but it looks kind of vigorous:
Sangre de Cristo mountains, start at the Ducket Creek Trailhead and head south on the Rainbow trail. Turn right into the mountains on the South Brush Creek Trail, and cross the pass into the Cotton Creek watershed. Head UP the valley, past Cotton Lake, and cross the pass. Hook up with the Rito Alto Trail and again head UP the valley and over the pass. You will then cross the upper San Isabel Creek drainage, and over another pass. Then make your way up to Venable Pass, but turn south along the Phantom Terrace Trail, and head down the Comanche Lake trail to the trailhead and out.
The 4-Pass loop in Maroon Bells Wilderness was recommended to me. It is much shorter than you requested, but it looks like it is easily scalable, connecting with a couple of other loops through the Wilderness. Look at a map and the "lollipop-shaped" loop near the Maroon Lake Trailhead is obvious. The other loops run to the northwest of the 4-Pass Loop, and are also obvious on any trail map (Trails Illustrated or Sky Terrain both show them.)
I'm still researching several other options- I'd like to do a loop around the Mummy Range in RMNP, if I can find a way that it can be done. Unfortunately it is looking like I'd have to cross private property.
I'm also going to look at the classic Chicago Basin hike (also in the Weminuche Wilderness) which is a sort-of-loop around the Grenadier Range with side-trails hitting several nontechnical 13-ers and 14-ers. Bonus- ingress and egress is via the Durango and Silverton narrow gauge railroad. The loop is 39 miles, but that doesn't include the peak-bagging.
Disclaimer- I have done NONE of these hikes- but I am planning to.