Can you specify your needs a little bit more:
- does "physically inaccessible" mean, that wiring is also impossible?
- is it possible, to have a hub-kind device, where the SAM3X8E-devices can be cabled to, which itself has another connection
- How many devices do you expect?
One rough idea could be JTAG:
It is no problem to reflash the DUE with OpenOCD. As JTAG allows chaining devices, it should be possible, to connect several SAM3X8E in a chain, using one JTAG-connector to flash them all.
(http://www.atmel.no/webdoc/avrdragon/avrdragon.section.sqr_osd_lc.html)
I have currently no idea, if openOCD is available for OpenWRT. If yes, there should be a lot of cheap devices out there, which could act as gateway-hub.