Hmmm. Had to think about this actually - I knew *what* needed to happen, but I had to think for a bit to remember *how*. Something I did at work the other day reminded me how much my skills have atrophied...must do some work soon!
Anyhow, first up: here's an optimised version, at the size you're using it. Filesize is about 75Kb.

Actually, it is showing a little ghosting - and I think I've placed the animation a little off-centre. Not to worry - here's how to do it in ImageReady 7 (the version with PS7).
1) Open your transparent, no background animation in IR.
2) Select frame 1 and add a new frame. This will be the same as the existing first frame.
3) Insert the background. There's a few ways to do this - I just dragged it from the background image file into the transparent animation.
4) Make sure the background is at the bottom of the layer stack.
5) In frame one, make sure that the only layer that's visible is the background you just added.
6) Right click on frame one, and select "Restore to background". This makes the content of this frame the "background" for the whole animation, provided you...
7) Select all the remaining frames, right click and select "Do not dispose". This means they all use frame 1's background as their background.
That's pretty much it. This way the gif only contains the difference between this frame and frame one - not much in this case. You can have different frames set to "restore to background" if you have different sections to an animation.
UPDATE: had a quick play and remove the ghosted frames. This allowed me to up the colours to 128, still at 75Kb.

Hope this helps!