I have done the overnighter on the Middle Fork and have paddled the South Fork at pretty high flows a couple of times. Depending on what you are looking for, I would recommend the fly-in on the Middle Fork Flathead. It has some good rapids (IV) lots of chill rapids (II-III), plenty of very scenic, melllow floating and great wildlife. The fly-in is spectacular and relatively cheap. (Red Eagle Aviation in Kalispell is my recommendation)
It is not that long (30-odd miles), but I would recommend taking your time, as it is quite impressive in there. Maybe 4 days with some relaxing and sidehikes if you can pull it.
South Fork Flathead is very mellow or flat for the multi-day section, which requires a rather expensive horsepack in. The Meadow Creek Gorge is at the very tail end of the run and can easily be done by hiking in from the bottom. I have only run it at high flows (+11,000). It is extremely intense, though not overly technical. A swim would be god-awful, if not fatal, as the boils, whirlpools and compression hydraulics are what make it class V. Very few exit opportunities exist in the 2+ mile stretch leading up to the gorge proper and getting out of the river would be tough for a swimmer. If unpredictable, difficult whitewater with high stakes is not what your crew is looking for, it is simply not worth it. If this excites you, the beautiful, mellow 50-mile float capped by something you will not ever forget may be right up your alley. You will not see anyone else on the upper stretches of the S. Fork at high flows, as the fishing is not great then. Lots of wilderness to enjoy. You can hike out the last 3 miles around the gorge to the parking area if everything but the gorge sounds good. The shuttle for this trip would be absolutely ridiculous, as the drive around the reservoir alone will take just shy of a decade.
North Fork - Never hear anyone talking about this one. Maybe that is a good thing. I do know it does not have much in the way of whitewater. I have a friend who knows the area well and would be happy to get you more info... email@example.com
I highly recommend the area. It is beautiful and either trip would be worthy and memorable. Drop me an email if you need any more logistical info. Have fun.