The problem with the range of the P3 SE is it's limitation under CE.
You can read about it under the P3 SE threads.
I'm not sure but I think i saw you can manually switch to FCC inside the remote of the P3 A. But better look it up yourself.
Youtube is a good source for gaining knowledge about your drone, when reading through forums can sometimes be exhausting.
If by color bands you mean the attached stickers, my P3 SE came with golden ones on it and a set of different colors in red, silver, golden and a real shabby looking purple.
So I guess relying on the colors isn't really a good way to identify the versions.
The P3SE is also not compatible with the DJI goggles but if you use the module your P3A is. The picture shows my remote which has no upgradable bay at the back. Please excuse the bad lighting.
But since you are connecting it only via HDMI I guess head-tracking won't work for you, sorry.
So without this function the DJI goggles are pretty overpriced so just get some fatsharks or eachine goggles, I recommend.
I have no experience in FPV so far. So don't rely on my words.
Also here Youtube may be a good source for finding out what suits you. They only need to have an HDMI input-port.
Channels like Half Chrome for example will help you decide:
Half Chrome
or Joshua Bardwells Channel:
Joshua Bardwell
For flying in FPV via the HDMI-port you must be aware of a little lag. The transmission is digital so it is not the fastest one.
The HDMI-output module has a resolution of 720p.
Don't expect anything like you can see from a racing-quad.
They use analog transission which is not high def.