I've realized that this game is the perfect game to own digitally, but I've already have been playing on my physical copy for months now. Is there any way to move my town from my cartridge and use a digital copy instead?

Wouldn't a SD card work? I haven't used my 3ds enough to know if that would work.

I think I remember hearing that there is a way to move from one medium to the other but not the other way around. I can't remember if it was cart to digital or digital to cart that you could move.

I think there's an app on the eshop that lets you pull a save from a cartridge game to a digital game. Not sure if that's possible with Animal Crossing specifically, since Nintendo has always been cagey about letting you do anything with game saves from games with online components.

Update!

Here is Nintendo's explanation of their save data transfer tool. I looked at their list of games that don't support it, and New Leaf isn't on that list, so I assume it should work for you.