I paddle a rented Q-16 solo, paddling from the front seat. I'm not sure I understand what you mean by being "squirrely" on flat water?

I've found that if I keep the heaviest pack the closest to the bow, it handles okay considering the "solo" seat is a little too far back for optimum handling.

It's slower than a true solo for sure, but with my faithful double paddle, it's an acceptable for the tradeoff of stability and load capacity and
ease of loading.

I did paddle an older Tranquility one time and it was the only time I've went over solo.
The newer models with the sliding seat and height adjustability might be better stability wise, but I'd rent one and bring all my packs along and see if they'll fit in the canoe without sticking up becoming a wind catcher and even more important raising the center of gravity.

I had to lay my one of my full size packs sideways and the other was flat but sticking way up above the gunnels.
I never felt comfortable because it was so unstable I knew the slightest mis-step I was going over.

If your gear is solo size, then that may not be as issue, but I'd try before I buy for sure.

When I buy a Q-16, I'll move the seat a little more towards the center and relocate the yoke, so I can remove the front seat and get the load even further toward the bow when solo.
I took the "front" seat out this year on in my rental, and I noticed a significant difference in handling being able to slide heaviest pack closer to the bow.

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Solo Tripper the Q16 I have only has 1 seat mounted midship. It was setup for solo only. I have thought about relocating the seat back several inches to see if that would improve the tracking.

A flat bottom boat will slide side to side easier than one with more of an arc in it's bottom cross section regardless of the rocker.  Maybe that's what's happening??
Plus ST uses a kayak paddle so he's limiting the need to switch sides for course corrections.
Maybe you should try a kayak paddle first??
Or work on your J stroke with a straight blade?
A good J stroke won't slow you down like a rudder does, and can be very enjoyable.

I read ST's Redrock link and it's probably right about using a J stroke sitting in the center. If you've in a flat bottom boat it'll side slip more than turn. But I know from experience that it works fine in a boat with a more rounded hull, i.e. Argosy, Voyager, Racing C-1. But SR are usually more flat bottom so the J may not be the answer.

Lucky me......I never test paddled anything other than having had a Coleman plastic canoe and went and bought a Merlin, then drove to the Q without having even tried it........ that was a decade ago and I have never regretted the choice. Good all around boat.........

I rented a Tranquility two years ago and loved it. Beaverhouse- Cirrus - Kasakokwog- Quetico - Beaverhouse.  I wouldn't want to ever pad sf le another solo.

I'm 6'-2", 225, a duffer that loves paddling, sit, hit and switch with a straigh shaft.