Glad to help, Ethergore,
I'm not a user of digital mapping software to any real degree. Not exactly a digital illiterate, but closer to that category than I'd like to be. I was raised and trained on paper maps and at age 59, I still hold a great attraction to them. So while I can't give you a gps track, offer further suggestions as noted below.
Following your track on a Google Map, I see your descent from Red Rock Pass into the Centennial Valley takes the North Valley Road and runs it all the way to LIma. There's nothing wrong with that, and Lima is rather more of a town and resupply/fuel point than Monida is. The route across the Centennial Valley I've read most about, however, is along South Valley Road, aka MT or Beaverhead County Route 509. I believe South Valley Road is more along the foot of the mountains forming the Continental Divide and is somewhat higher up than North Valley Road, providing long vistas across the Upper and Lower Red Rock lakes and the Lima Reservoir. I haven't a clue which of the two may be more enjoyable to one's tastes and preferences, however. Anyhow, South Valley Road connects to I-15 at Monida, so Lima is just north a piece for fuel, food, etc. I think there is a very nice and fairly new Interstate Rest Stop at Lima, too.
FWIW, my initial suggestion intended to mention slabbing up I-15 from Monida to Dell @ MP 23, thence taking the Big Sheep Creek Scenic Byway through and along the Tendoy Range up to connect to MT 324 west of Clark Canyon Reservoir. The BSC byway is, however, another 55 miles of graded gravel and two track, and would thus take maybe 4 hours as opposed to simply slabbing I-15 to MT 324 @ MP 44. You can't really go wrong on I-15 along through there, either, as it's a beautiful drive in and of itself.
Down to the meat of your question: The suggested route from Grant, MT over to US 93. Your track shows MT 324 running all the way to Lemhi Pass. This is incorrect, as today's MT 324 turns south a handful of miles past Grant and crosses into ID at Bannock Pass, thence down ID 29 (?) to Leadore, ID on ID 28. From MT 324 to Lemhi Pass is simply Lemhi Pass Rd. There's nothing wrong with Lemhi Pass, of course. It's one of my favorite sites in all of ID and MT. You can literally feel the vibe of Lewis & Clark's ascent and see for yourself the view to the west, which to their horror was mountains as far as one can see. But crossing into ID at Lemhi Pass causes you to miss the Big Hole, and we can't have that, can we?
So, to snake your way into the Big Hole, first pass Bannack Bench Rd running north off of MT 324 a shade east of Grant (which, by the way, does not actually exist--a closed-down store and a few houses and mobile homes--no goods or services as of 2011, anyway). You'll soon pass Mansfield Rd on the R and MT 324 will start to swing from about due W to the SW as you pass a prominent peak named Red Butte. You'll quickly arrive at Lemhi Pass Road on the right, and a very nice and informative parking area and viewpoint is on the opposite side of the road, calling attention to this as being the intersection of the Lewis & Clark route and Chief Joseph's route as he and the Nez Perce fled the Battle of the Big Hole some 40 miles to the north. Turn R onto Lemhi Pass Rd, but turn R at the "Y" within about 3/4 mile onto Brenner Road. Follow Brenner Rd for a couple of miles, past some very nice ranches, to Bloody Dick Road, on your L (I am NOT making this up--a particularly violent area settler named Richard was nicknamed Bloody Dick). Come to think of it, you may not actually see a sign for Bloody Dick Road, as I think Beaverhead County and the USFS tired or replacing the stolen ones decades ago. Anyway, Bloody Dick Road ascends the creek of the same name and enters FS lands, finally reaching Reservoir Lake and its FS campground some 15-18 miles from MT 324. You'll continue past the small lake and its CG (a very nice overnight spot, by the way) and will go through Big Hole Pass (one of several), thus transitioning from the Beaverhead River Drainage to the Big Hole River drainage. Soon you'll pass Skinner Meadows and Skinner Lake, site of the year 2000 Rainbow Family Gathering, by the way, and continuing northerly past the Van Houten NF CGs along what is now named Skinner Meadows Road will bring you to Jackson, MT and MT 278 (paved), in the very heart of the upper Big Hole.
I have searched for and not found a route paralleling the snowcapped Beaverhead Mountains along the west wall of the Big Hole from Skinner Meadows to Gibbonsville Rd, so to the best of my knowledge, you've got to pop out on MT 278 at or near Jackson at some point. And that's OK, because Jackson is comprised almost solely of the Jackson Hot Springs Resort, a nice motel w/ cabins and campsites, a very nice bar and restaurant, and an outdoor swimming pool fed by the natural hot springs waters. Have a look, they're on the Interwebs.
Again referring to my initial suggestion, there is a Gibbonsville Road running southwest off of MT 43 a short distance west of Wisdom, MT, where MT 278 ends in a T junction with MT 43. I think Gibbonsville Road can be accessed from Twin Lakes Road, which turns west off of MT 278 a little over halfway between Jackson and Wisdom. Gibbonsville Road ascends the north fork of the Big Hole River, re-enters NF lands at the base of the Beaverhead Range, crosses into ID at Big Hole Pass, and descends sharply into ID where the name changes to Daholega Creek Rd, ending at US 93 at Gibbonsville, ID, maybe 10 miles south of Lost Trail Pass, where US 93 returns to MT for the drive up through Darby to Hamilton and MT 38 over to Skalkaho Pass. You will see that simply remaining on MT 278 to MT 43 also brings you to Lost Trail pass, with the added attraction of passing by the Big Hole National Battlefield, a sobering place to visit if there ever was one. There is a May Creek campground in the NF between Wisdom and Lost Trail Pass, and it, too, is a fine overnight stop.
Just on the south side of Hamilton, MT, your track correctly picks up my suggested route up MT 38, passing Skalkaho Falls, to Skalkaho Pass, over into the Rock Creek drainage, thence north on Rock Creek Rd, FS 102, at the base of the Sapphire Range which you just crossed. You will note FS 102 takes a left just before a bridge over Rock Creek, where going straight for a few miles on paved MT 348 brings you to Philipsburg, a delightful town. FS 102 then continues generally north, just as your track follows, for 41 miles to I-90. The mileposts count down from 41 at the bridge to 0 at I-90, and the pavement begins at about the MP 10.
If I were to follow this entire route, I'd be sure to start with a full fuel tank at West Yellowstone and top off at Lima and Jackson or Wisdom, then again in Hamilton, where a lower price fuel stop is a couple or three miles north of the MT 38 turn-off, right in the middle of Hamilton's downtown.
I hope this is helpful, and I most certainly hope you'll post a trip report, regardless of your final routing choices.
Any further questions, fire away.
Foy