I ran into this same issue on my last trip into the Q.  We ended up with 5 people when a group member pulled out at the last minute. When deciding between the options of 3 canoes or 2 canoes, these thoughts came into play:            
1) We had a couple newbies, so inexperience in the stern would have been a factor.  We had 2 members of the group that were the most capable.
2) We thought taking only 2 canoes might allow us to carry everything in one trip across portages.
3) We didn't think anyone would be able to keep up solo.
3) No one wanted to sit ackwardly on the canoe bottom for 7 hours at a clip with a canoe bar in their back.

We ended up taking 2 canoes, and we managed every portage with 1 trip across (a huge plus  ).  The same 2 paddlers manned the sterns the entire trip, while the remaining 3 switched off equal time between the bows and the middle of 3 person canoe.  It turned out fine, and we said we were glad having done it that way.  The only downfall was trying to fish 3 people out of a canoe after we found that deep water walleye hot spot, but we were able to pull it off.  At one time we actually had a lake trout and 2 walleyes on the 3 lines at the same time.  Pandemonium in a canoe.

Lots of recommendations for the solo option, but I guess it's no surprise because many on this forum typically travel solo.  I guess this could be a good trip to try out solo paddling, but I'd recommend a trial run on a lake near your home.  That way, if you hate it, you're not stuck for several days.

Although I'd love to try it, I have not paddled a solo canoe, but don't mind soloing in a tandem canoe.  If you decide on 3 people to one canoe, I'd highly recommend the Souris River 18.5' with 3rd seat.  Many outfitters in Ely have it, and it's very spacious and comfortable for 3 people.  Frankly, 3 people to a canoe is my prefered travel method, as it helps with single or 1.5 portaging.  I dislike a group size of 7 the most.  With all 3 people paddling, a canoe will flat out fly, even in a headwind.  However, fishing while traveling does indeed pose a challenge.  Since a few members of our regular group don't fish, have no interest in fishing, and don't even really like the taste of fish (heresy, I know!) it isn't a problem.  They get to relax in camp, explore the woods, catch up on reading, or whatever else they like to do.  Meanwhile, we have enough canoes to have 2 fishers in each, and our travel speed means we have a lot of time to fish once we get to camp.  Just take stock of your group's personalities, abilities and goals to make your decision.

 They make portage yokes for kayaks, they have them in the Piragis catalog.
 I wouldn't under any circumstances put a Newbie in a solo canoe, at least not in a place like the BW/Q.

I paddled a SR Tranquility my first time solo in the Q. It was an early model that Quetico Dave had for rent. It was a nerve racking experience for the first few days. Mid-May, the weather was up and down. It was very tippy feeling to me, but I got used to it after a few days of trial and error.
 
The worst part, was my packs which are fine for tandem width canoes, didn't fit in solo. I had to turn them on there side, which left them sticking above gunnel's, which I really hate. In crosswinds they caught air like sails and added to the drama
 
My one and only dunking came in that solo canoe. Part bad judgment on my end, high center of gravity on the SR's.
 
The new models have adjustable height seats. They also seem to have a different seat frame set-up, compared to the old one.  
 I'd make damn sure your packs can be stowed BELOW the gunnel's, and keep the seat as low as you can, and still be comfortable.

No one has mentioned it, but as a dedicated double paddler, I'll throw it out. Unless you have kayak experience, you'll have a learning curve with a double kayak paddle too. The solo will carry more gear, and is easier to unload and portage. You could always carry just the packs that fit in easy from the other canoe(s). With an experienced paddler/fit paddler, that solo with a double paddle should be able to keep up with a tandem at a normal cruising pace once the solo paddler gets the hang of the double, which he will have to do if you go the kayak route.
 
I rent a SR16 Kevlar tandem, and paddle from front seat. I won't say I can keep up with a tandem that's going all out, but I move along pretty well, fast enough for most situations.

Another very important thing, is making sure your loaded correctly. Slightly bow heavy will work in most situations, other than a real strong tailwind.  Being out in open water is no time for wishing you had the right load set-up

Thanks for all the great  input.  Here's a little more information--I hope people will continue to chime in.

1)  By "no solo experience", I meant "no experience paddling solo, period." 

2)  Not newbies (about 10 Q trips), but not accomplished technical paddlers.  I know the J and C, and occasionally use the pry and draw but that's about it.

3)  Unfortunately, I don't think that kayak will be an option due to logistics.  Our outfitter doesn't appear to offer them (and we're going directly from Minneapolis to LLC).

I'm tempted by the solo (I'd be the one in it most of the time), but am concerned about staying upright and keeping up.  I like swimming as much as the next guy, but . . . .

Sounds to me like deep down, you *want* to solo but you just need a push to convince you it's OK...or maybe it's your friends that need convincing that you won't slow them down?

Soloing isn't nearly as difficult as it seems when you've never done it.  I was a diehard tandem canoeist until last year when it was either solo or stay home for me.  I took a 9-day solo trip and I'm very glad I took the plunge (figuratively speaking only).  Up until the moment I shoved off I had no experience in a solo canoe.

The butterflies lasted about halfway across Inlet Bay on Basswood.  After that I felt very comfortable.  I tried a double-bladed paddle but that style of paddle uses different muscles, so I switched over to a single-blade and didn't lose all that much speed. 

I'm in decent-but-not-fantastic shape for my age and I had little difficulty keeping up with tandems that were heading in the same direction as me down the S-Chain.  They weren't racing me or anything, but they weren't loafing around either.

I got into some hefty headwinds and was still able to keep a decent steady pace of travel.  I even accidentally got into some surf that only an idiot would try to canoe thru and I managed to stay afloat until I could reach calmer water.  The key is to stay loose in your seat, keep your torso centered and vertical and let the canoe roll with the waves under you.  The canoe WANTS to stay upright.  Usually when it doesn't it's because someone panicked and made a dumb move.

4 travel days on your loop is not going to kill you in a solo, either.  I've done that same loop several times and none of the days is particularly difficult.  You'll do just fine.

I'm in a party of 3 this year.  A tandem plus me in a solo.  I can't wait to get out there again in my own canoe!