Hmmm. Well nobody answered my query so I've been experimenting and think there are a couple of ways to go....but probably not what you're thinking Joe.
I had a nice 10-17 day, with a 7.0 UL and at the spot where we get the best inland surf. Nice waves, sets of 4-5, clean faces with a lot of curl, don't close out all at once. So I was lightly-to-moderately powered, depending on gust or lull.
In that gusts powered-up, the 11'5" in the straps is good for wave riding with power-on bottom turns and cutbacks (which was the top of my neophyte skill level). In the lulls, the 11'5" out of the straps is good for surf-sailing (schlogging out, catching a wave to ride it back in). I did manage to do a clew-first sail-and-body 360 while surfing a wave, so I was pleased with that.
My SUP (Pacifico Wave) is a nice board, but really doesn't do the powered-up bit that the 11'5" does. I was a bit concerned about the footstraps being in the way, but it hasn't been a problem (I have the front straps full out and back / single back strap). So of the two, I much prefer the 11'5" (and I think the construction quality is higher).
But perhaps the most interesting observation I have is that both boards, and especially the 11'5", really lure you back into the shore break. The PW is not at all good or fun to get planing in swell/chop; the 11'5" is much better at that than the PW, but it's not particularly exciting as it is slow, there's no jumping, it's just B&F in the swells. That ends up not being nearly as much fun as getting inside where the waves are jacking up and breaking. Because it's designed for surf, the 11'5" is quite at home in the whitewater, it's not at all hard to tack it in the tumble dry section (I think the PW is OK but more bumpy a ride). So in 10-15, at 190 lbs, I doubt you'll be doing much jumping (on a 11'5" or any other); in 15-20 you can begin to jump, but not with a Kona or your SLW. The F122....you probably can when it's near 20.
So the 11'5" is much different than anything you're doing, because it's truly a board for surfing. I'm not sure if it adds much, given that you've got the 12'6" SUPer, though if the SUPer and my PW are remotely similar, then the Kona 11'5" is way different (and in my taste dramatically superior to an SUP). Because you're on fresh water, and substantially bigger than me, I would not go for the 10'5" unless you only want the powered-up mode.
If you don't want to do any schlogging out / surfing back, I'd suggest you find a place to try it - quite laid-back, very entertaining, still is sailing, it's nice stuff. The SF is a very nice sail for this kind of stuff, btw, because of its soft feel (matches a surf sensation very nicely). I'd get an RDM if you're going to do that, though.
I think if you get the 11'5", when you go to the big lake, all you'll want to bring is the 11'5" and your Taboo.