Normal maps don’t use the same compression as RGB Or RGBA and in fact by default throw away the B channel and do a higher quality compression on just the RG. I would not recommend packing them, especially if you’re using arrays they will share a single sample anyway. If you’re not saving memory or samples there’s no point.
Frankly there’s no good way to load 60 normal maps into memory all at once. You can really only reduce the number of frames, the resolution or the depth and all will likely adversely effect the quality of the animation.
Normal maps are meant to cheaply add lighting detail, if they stop being cheap it begs the question of why are we using them.
Without knowing the exact nature of an animation it’s hard to recommend an alternative. But for example vertex animation can cheaply animate real geometry via math or textures.