Well, I got that caltopo made quicker than I thought. Here's the skinny:
Part I: The "stick" of the lollipop for the Bear's Tooth hike is the easternmost red section. At 5.07 miles and nearly 1,500 feet of elevation gain, this might be the better part of a day, depending on how early I can get to the trailhead.
Part II: The purple loop is the exploration of Black Canyon Lake and the country all around Beartooth Mountain itself, including Spirit Mountain and Sky Pilot Mountain, numerous lakes, a lot of climbing (especially over that pass at Beartooth Mountain) and essentially no trail at all to speak of for most of the route. At 13.78 miles, and with nearly 5,000 of elevation gain, this is either a very long, hard day, or better yet, I'll stop somewhere partly through it at one of those lakes.
All in all, I see this lollipop taking 2½-3 days. The total mileage is Part I x 2 + Part II, or 23.92 miles. Not a bad little loop.
Part III: Assuming that I'm starting this fairly late, after doing the loop above, this is the "stick" of the second lollipop. It's 9.51 miles long, and gains over 3,000 feet of elevation gain itself, so it's not a picnic, exactly. I would tend to see it as the better part of a day's hike by itself; if I can't start 'til late, I need to camp somewhere inside the trail; maybe at either Elk or Rainbow Lake. If it's really late, I can always camp right there near the trailhead at Rosebud Lake somewhere.
Part IV: At 18.73 miles, this is the real meat of the whole trip. Continue on the "Beaten Path" trail to Fossil Lake at which point you break cross country to get to the Aero Lakes, go through the valley between Mount Villard and Cairn Mountain, have a good, up-close look at Granite Peak (the highest in Montana!) before heading back down to Big Park Lake and rejoining "the stick."
Part V: This little spur is completely optional, but goes up the hanging valley to the wonderfully scenic Martin lake, Glissade Lake, etc. The climb up to the hanging valley is supposed to be pretty brutal, but once you're there, it's not too bad. At only 3.11 miles, this is just either a day trip, or a nice, secluded camp site if I start it in the afternoon.
In total, this second lollipop is 43.97 miles (37.75 if I forego the optional hanging valley spur) which is still a good 4½-5 days. Both hikes together are, at a minimum, 6½ days, more likely 7½ or 8. That's a long time in the wilderness (I tend to find that after 4-5 days, I sometimes have had enough and am ready to come back) but after missing 2016, and assuming that I've been successful in getting in better shape before starting this year, it'll be doable. Plus, that means that I won't need to worry too much about coming back this way anytime soon, and I can see something else in 2018's summer.