Add pre-rendered fire to scene Situation

I am working on a visualiser that sprays fire at the start of the drop


In my Scene there is a 2D animated background, multiple thousand frames long
I have two fire fountains which spray two times for about 80 frames within the former animation time
This fire fountains takes about 2 hours to render each time these frames are hit, and the fountains are always the same
The camera constantly shakes


The scene from the side (ignore the overlap of the fire with the other stuff, it doesn't matter)

From the camera (beware that it shakes, so it won't stay exactly the same)

Rendered


Goal

I want to pre-render the fire and then somehow insert it to drastically reduce render time, and I can't simply layer it because the fire is 3D and the camera moves.
I have no idea how this can be achieved and would appreciate any suggestions :)

Progress

I now have this node setup, but I don't know how to get rid of the black background. Everything I found was for cycles.
You can pre-render only the particle effects, then add a frame of the animation using Add Images as Planes (enable the add-on).

Then parent the image plane to the backdrop and change the source from a still image to a video sequence.

You can separate them out into different layers and then composite them together in the Compositor.

If you render with alpha, use the Alpha Over node. If you render against a black background use a MixRGB node set to "add".

The Compositor will also allow you to add things like glow effects if you want by using a Blur node.

Probably worth testing your workflow on a small number of frames first to make sure everything's working before rendering the whole thing.