Hey there. I'm the one looking to transplant a V6 into my base '06.
Current status: The Chevrolet Captiva (Saturn Vue) I bought at salvage auction and intended to be a donor is in too good a shape to be parted out. My wife convinced me to fix the car and either use it, have her use it, or sell it as a repaired car.
I've been thinking about an even more ambitious project - a V8 install. Not an ordinary LS one (LS's are so expensive around here! Like $10k expensive), but a Volvo B8444S - 4.4 60-degree DOHC V8 off a scrapped XC90 - that I already own and is at the machine shop for 4 years already, just waiting for me to go there so I can assemble it together with the shop assembly tech.
But if you decide to go the V6 route, you will be the first one probably. Or at least the first one that the fora know of. I researched this path quite extensively. The best engine would be the LY7 3.6 High Feature V6 out of a rear-wheel drive GM vehicle from around the same era as the Solstice. Second-best would be a front-wheel drive version of the same engine. That's why I got a hold of the Saturn Vue. Actually my story goes deeper as I first had gotten hold of a 2005 Chevrolet Omega (Australian Commodore) -- the precursor of the '07 and later Pontiac G8 as sold in the US. This car is RWD and the only GM 3.6 LY7 RWD model that was ever available around here (there was also the Colorado-based Trailblazer but they sold poorly compared to the turbodiesel version and are rare to find in parts-car condition). The car-carrier truck it was being transported on its way to me caught fire, so total loss and 6 months struggle to be repaid by the insurance. Then I couldn't find another Omega so I wen with the Captiva/Vue which has the same engine but is FWD.
If you live in the US the range of rear-wheel-drive vehicles equipped with the LY7 engine widens. Off the top of my head I'd say the '09-ish Camaro V6. Some Cadillac models (CTS I believe?) too.
Then, there's the question of the ECM. The earlier 2.4 Solstice used the E67 ECM which was also used by LY7-equipped vehicles. That means there is a V6 operating system (OS) that could be flashed into the Solstice ECM. But most likely the ECM will expect to be communicating to a BCM (body control module) from the V6 car, not from the Solstice. That also has to be sorted out. You'd need to make a new engine harness to go with the extra 2 cylinders (2 more coils, 2 more injectors, 1 extra O2 sensor etc.).
You would also have to solve the bell-housing on the transmission which I think is not a direct bolt-on to the LY7 (I might be wrong) - a custom adapter plate might be enough, or you might need to fab your own bellhousing. I imagine a Camaro bell housing will be helpful here.
It is a difficult and long, slow path but you'd have the most unique Solstice around. And with 6 cylinders it would sound a bit more similar to the German (Z3/Z4) and Japanese (350Z) competition the car had at the time. Also the power your V6 would make, in stock form, would be less than a well tuned supercharged 2.4 or a GXP engine. Unless you also had the V6 prepared with cams/injectors, or supercharged or turbo'd your V6, in this case you could have power levels between 300 to 450hp depending on how extreme a setup.
I'm willing to tackle the challenge - be it Volvo V8 or LY7 V6, whichever I choose in the end - but I am fully aware that I'll probably have the car in a non-running state for 1 or 2 years.