It should be possible to build what would in effect be a 360KB drive emulator, which would also have a 1.44MB controller and drive. You wouldn't be able to store more than 360KB on the 1.44MB disks, and you might have to do some inline remapping of the FAT to handle the differences in sector/track sizes. Sounds like a fun project!

As for converting the original 360 disks, find an old PC with both size drives, and copy old to new disks.

Good luck,
Dennis