Here is my question though. Even though this prop has a total of 1200 pixels, they will most likely never be lit at the same time. For example, it may only be one (or 3) of the singing faces singing. Or it may just be the arches lit.
Your thinking is not incorrect, but what happens next year when you want all of them white at the same time? Will you want to rework everything, or even remember they are under powered. I personally power everything to handle full white at 70% power, and only run 30-40%. That leaves me a cushion and I never have to troubleshoot power issues each year. Are you trying to get by for a few days until more parts arrive, or are you trying to make this permanent? I would do it right if you can, but you can push it if you need/want to.
I'm assuming that the power limitation would only apply if I light ALL of the pixels at once? Not if only certain elements/pixels are on at once?
Correct, but see above answer.
Per the power calculator from WiredWatts, in theory, a 350w power supply "should" be able to power ~900 pixels at 50%. Still not enough to turn every pixel on at the same time, but possibly enough to run it in a show?
I run 2000+ pixels off a 350w at 30-40% power. Depends on the lights, but would expect 900 lights to easily run off 350w
My other question is if you have any information you can share on power injection. Like how do you house and wire the additional power supplies?
I try to keep my strings small enough I do not have to power inject. Some models need to be power injected or the programming effects do not look right, such as long straight strings on my eaves. When I need to power inject I use an empty controller port. Not the cheapest solution, but I can move the model from controller to controller with ease and makes everything easy to hook up. I basically take a 3-3-3 tee and remove the data pin from the power injection source with pliers. Not suggesting you do the same.
There is no right or wrong answer provided it works. Some have dedicated power injection boxes, some install power distribution boards in their controller box. Really depends on the individual needs and preferences. Since I rarely power inject, I would not be the best source on this.