Perhaps an underipe Quince, Pseudocydonia sinensis?

Immature hedge apple / Osage-orange? Don't know if they're always bumpy or not...

The osage here are already looking very brain-like. They look kinda brain-like inside too....and firm, not like eggplant-like. I'm also very sure they wouldn't taste like pear. ;) Not osage orange.

FataMorgana

could also be a white guava, but to me they taste nothing like pears.

Thanks, Fata. All we ever did with those was hit them with a baseball bat, great fun that! So I wouldn't recognize a cleanly-cut one.

I know someone who uses the osage fruits in herbal extracts so I know well what the inside looks like. Baseball bats....well they are softball-sized! ;)

First impression to me was a guava as well, but I'm unfamiliar with the fruit so don't know.

FataMorgana

All the guavas I've ever seen had a very distinctive fruity smell. I also think this looks like guava. But that seems unlikely if it was growing in Maine. Can you tell us where you got it?

Here is a link that might be useful: Guava