All three had weird artifacts in their animations (specifically the idle animation). In the case of Haxorus it just turned out it happened on frame -1, and thus I could safely ignore it, as all animations start on frame 0. I wasn't that lucky with the other two.
The first time I attempted to use the Aggron model, its left leg disappeared altoghether for a frame mid-animation. Deleting the problematic keyframes just corrupted the animation further. This issue happened in both Blender and Unity. Strangely, when I repeated the process again, this no longer happened, so I'm guessing it was an occasional bug with Spica (which by the way I'd like to, at least, be able to predict as I don't have the time to check if every single Pokemon is exported properly).
However, now Aggron has a more consistent problem with the bottom part of its feet and middle toes. In Blender, nothing happens with them when the model is in a T position, but just as I hit play these faces disappear. I don't think it's a normals problem because if it were the faces should be visible from the inside of the feet, however they are not. But they aren't deleted either, because highlighting the armature in the hierarchy resets the model to a T position and the problematic faces just reappear. As expected, saving it and then importing to Unity also causes the faces to disappear. Importing the .dae directly to Unity has different but equally unavoidable artifacts with the feet.
Garchomp is far more broken than Aggron however. Importing its .dae file to Blender breaks the animation completely. For some reason however, importing the .dae file to Unity displayed its animation perfectly. When I compared the armature hierarchy in both programs, it turned out that an awful lot of bones were missing in Blender. Unlike the problem with Aggron's leg, this problem is very consistent no matter how many times I repeat the process, and have no idea how to restore these bones nor why they are deleted from Blender while Unity recognizes them perfectly. Saving the .blend file and then importing to Unity results in a completely empty model file, with no mesh, no child objects, no animations, and not even an avatar. Nothing.
Please note that while I could work directly with the .dae files, I need to be able to modify the models in Blender and reuse the original animations with the modified models. As far as I know .dae and .blend files can't share animations because the hierarchy of the bones is slightly different: .blend models bones are all children of an object called "Armature", which is absent in the .dae models. I believe this cannot be changed as I haven't found the way.
Perhaps I should state that all animations are displayed correctly in Spica, so I can't really figure out where the actual problem is. Google didn't help much either.