I'm inheriting an old single shot 22lr rifle. It was my great-grandfather's well over 100 years ago. Currently it's in Pennsylvania with my father. It has no serial number.

How do I legally get this gun to me on Maui?

https://imgur.com/a/UxNEEbe

The best plan so far was to have my father fly it out to me and then take it into the police station for a transfer. Does that work? Are there more steps? Do I finally have an excuse to get my C&R license?

IDK about MPD but Honolulu will make you engrave a serial number on a firearm if it doesn't have one--I bought a Winchester .22 that had the shop's rifle permit number (the "G#" in red) recorded as the "serial number" of the gun.
It was electro-penciled on the receiver below the stock line so you can't see it after it was reassembled.  MPD may require the same thing--you would have to check with whomever is in charge of firearms registration about that.

Since you don't have the firearm yet you could check with MPD regarding the whole process of getting it registered to you--that would be the definitive information you would need to legally obtain and possess the firearm.