OK. Mindthreat: you need to give more details here, and maybe rename thread a bit - because pseudo 3D background - even isometric platformers are called often 3D. What color depth is in question ? I really can not judge it by those blurry shots.
But let's assume it is 256 colors. Then we have 320x240 bytes per background = 76800 bytes. For 25 fps it would be: 1920000 bytes/sec. Falcon IDE can about 3.2 MB/sec, so only background draw would eat 60% CPU time. But maybe 10 fps would be enough for background draw, while sprites with more fps (some game have different rates for background and sprites too).
I made some tricky solution for achieving about 3.6 MB/sec on STE machines, so in theory that would be 2x more on Falcon. But question is would it work with 68030 CPU. Plus, it needs some wire cutting in machine, so not an option.
Let's calculate how much MB takes 1 room: It seems about 1500 px width. If we use 2px step while "scrolling" - or panning is the right word ? Then we need 750 frames, so 750x75KB=some 60MB . Clearly, it can't fit in RAM.
So, yes original idea of CD is the solution, but now we use rather Flash cards, of course. It reminds me on laserdisc games - like Firefox. However, that was pretty much different, because we had analogue signal from laserdisc, and then mixed into it computer generated sprites, some text ... Special HW needed.
I'm not sure how CD Amiga worked, but I assume that CD was only for data storage, and not doing video - correct me if I'm wrong.
So, back to topic: solution would be using CF cards - on Falcon it is simple, it has IDE port. Then need to decide concrete details about resolution, color depth, fps for background - keeping in mind to leave enough CPU time for other things.
I don't know about Jaguar. It is faster for sure. Question is how hard is to add IDE port to it ? Probably possible relative easy on it's game cartridge port.
English language is like bad boss on workplace: it expecting from you to strictly follow all, numerous rules, but self bending rules as much likes