And if the Flash were removed and the stored program area copied to a 'stored file' that would not be a complete solution.
The Teensy Loader wouldn't facilitate programming that to other Teensys? Unless that 'stored file' could be restored to a usable .HEX file? Otherwise one or more Flash 'duplicate' chips could be made from the working donor, but they would need to be soldered in place onto recipient Teensy units?
Then there is the question of the recipient Teensy and bootloader detecting a mismatch of the MAC/Serial number of the MCU on the recipient having some conflict if the Flash were serialized to the original donor MCU. This may not be the case and PJRC could confirm that. Maybe that could be avoided by only doing partial Flash copies of the code area of the Flash and leaving the upper areas untouched and returning the same Flash to the recipient Teensy. There is the one block marked Read Only in the flash with the factory Restore code and the EEPROM area.
Though perhaps a custom version of FlasherX type programming could be made to manage non-Hex but rather Block writes of the donor code area to the recipient Flash rather than external flash writes with chips removed and restored.