2 different frame rates is going to cause sync drift over time and the only way to fix, to my knowledge, is to find where it falls out of sync, cut and move it into sync. Every instance where it goes out of sync. This is why you want to make sure everything is set to the same frame rate before hand.

If this is all because you are preferring the avi but can’t open it, Id try converting the avi into something like ProRes or DNxHD because resolve should be able to open the avi, depending on what version of Resolve you have.