3rd the ATEM TV Studio. I'd rent if possible.
For overlaying text / graphics you're referring to a downstream keyer (DSK), which that Blackmagic box has built-in. This is how TV report's names and graphics
fade in and out during live TV broadcasts (among other things). Captions are typically generated by a "Character Generator" which unfortunately the ATEM doesn't have built-in. You'll need something else to generate the caption text as video and feed that into the Blackmagic box as well during each show (a computer running
power point would likely be the easiest / cheaper source to do this). The text will generate as a black
screen with black text, so you'd use one of the Blackmagic box's upstream keyers to remove the "black color" same as a green
screen works. That way you get white text shown on top of live video.
You'll need a laptop running Blackmagic software during the show to control it, but that shouldn't be too much of an issue (the other way to control the ATEM is using the 1M/E Control panel, but that's extremely expensive an unnecessary).
Do not route live video into a computer if at all possible though. This is frequently attempted by churches for
IMAG and theatres for special effects like you're describing, but the
latency always too high and distracting.
Lastly, I would try ahead of time plugging your camera directly into your video projectors before looking into the ATEM. Depending on the number of conversions you're already doing, the
latency of the
projector internal processing may already be too high.