I noticed that your animations include part whcih animate acroos the tile boundaries. That is not good idea, and probably should not have been separated in the first place. if you just place the two animations side-by-side on an HTML web page, the two animations will be disjoint time-wise.
Why was it split in this way? I have seen animations like this before and associate it with Japanese teenagers. Does the style have a particular name?
A better way of spliting the animation would be to have a horizontal split for the cat at the top, then a vertical spilt between the bear and the wing, prehaps with a non-animated static image between to make them smaller (though that should not be a problem).
Maybe I need an example of separating an image into tiles, so the various parts animate indepandantally. This image may be a good example for this too, though may be a bit advanced as I also will need to work out a mutli-frame comparision to locate the areas with animations so I can then work out 'cut lines' for the tiles.
As the second part is more complex, I may do it after the first. EG: rejoin the bad split, then split it properly.
All that depends on having time to create new complex IM examples, rather than adding quickie little ones. Currently I am working on my video editing skills to make a reasonable DVD of my wedding (which was two years ago).
Okay back to your problem...
Dependence on too many things(For example:gif2anim,anim2gif...).
The "gfi2anim" and "anim2gif" are some shell script wrappers around IM, that takes an GIF animation (preferably coalesced in this case) and creates a sequence of seperate image files, as well as a special ".anim" file formated as "convert" options to let to recreate the animation exactly as it was. That is the ".anim" will preserve all the timings, offsets and disposal methods that was used in the original animation.
Using these scripts means you can coalesce and dissassemble a GIF animation, append each frame pairs and re-assemble the animation using the same timings.
Later I plan a another script that will merge two ".anim" files with dis-simular time sequences. This would allow you to keep the various parts of the animation separated for 'optimization' purposes. that is animated part A will have separate overlay frames to animated part B. This would be the ultimate 'merge two animations' program, not just an appender, but needs a lot or work to get there.