A lot is going to depend on your style of animation but it's a good suggestion to use the timeline feature (which is basically a version of construct animate within C3 as I understand it). Breaking your art down into parts and animating it there could work, but may also be tedious and if you've already done the animations then it's also double handling (I haven't really explored the timeline features much) - there was some software called "Spriter" which had construct integration and could allow you to set up bones/rigs and animate and then import into construct - this would be a good solution however I'm not sure on the compatibility with C3 and when I was experimenting with it I found the integration with construct pretty fiddly.
You could also experiment with using the timeline features to dynamically destroy and load in animations as needed - eg if you need a facial animation you could destroy the static face and load in an animated version and then when that's finished destroy that and load a static one back in. This might be a lot of work with events and there might also be visible visual delays as the animations load in if they are really big, but might be worth experimenting with.
Would also experiment with your export settings, sounds like you're exporting at a very high res, could this be reduced drastically but still look good? Experiment with the scaling settings in the project, you might be surprised at how good smaller assets can still look when scaled up.