Circle to Rounded Rectangle Morph Transition

Hello everyone! So on and off for the last couple of weeks, I've been trying to recreate my YouTube channel's "Subscribe" animation that was made by someone else for practice and to add in an updated logo. However, what would seem like the easiest part of it has actually been super frustrating for me: the circle to rectangle morph

I do have a decent amount of AE experience already but can't seem to figure this one out. I've tried a ton of tutorials and done the copy paste bezier path technique, messed with mask interpolation, changed first vertex, etc but I feel like I'm overcomplicating things. Anyone know an easier way to do this? Or how to just in general? I attached how it should look and how it looks with my version. Thank you!