just do our thing, engage with our users, and reiterate until product/market fit
^^ This.
It seems like you haven't considered the possibility that your users who haven't "jumped ship" so to speak actually use something that your competitor can't provide. You just have to figure out what that something is. Build a bunch of tests and try to gather data on what that something is.
Don't try to copy the competition. That difference could be your distinguishing characteristic.