Struggling to clip text to an animated path (NOT animating text to move along a stationary path)

I have been working at this for a good amount of hours across a couple days now and it appears that nobody has had the same question so I decided it's time to ask for some help. I'm new to After Effects (but I use Photoshop and Illustrator so I understand most of the non-specifically video things) and for this project I have a stop motion video I made from some pictures I took driving past a mountain. I cut out the sky in all of them and cropped it to a square so it's basically just the sillhouettes of the mountain rolling in and then out of the frame. (I attached the mp4 with no background if thats confusing) 

The issue that I haven't been able to solve is finding a way to have the text match the contours of the mountain each frame. I've tried a lot of options in the menu but it appears that no matter what I can't make the path mask for the text animated: like when keyframes are added and I move the anchor points it affects the path for ALL the keyframes. If I try to just make a shape layer path or a mask path and animate it with keyframes I'm unable to clip the text to either of them. All of the animation options (I may be wrong but this is what I've concluded) only affect the texts position, alignment, etc. on a stationary path. I'm wondering if anyone knows if it is possible to acheive the result I want in After Effects (or even any solutions in another software like Premiere) without having to create a path frame by frame in Illustrator put the text on it and composite that. Less than ideal as I have 348 frames lol. Thanks!!