OK, there's probably a workable hack for this.
It turns out that libcurl (used by the Flash Player and several other programs on the chumby) and wget (used by some other features) both use the same environment variables to set an HTTP proxy.
It is also that case that any non-interactive shell on the chumby uses /psp/.profile to set environment variables.
So, the hack is to append your proxy settings to /psp/.profile, something like:
export http_proxy=http://ip.of.my.proxy:port/
Now, the trick becomes how to get that line in there if you can't ssh into the device in the first place (because you don't have the proxy yet). Well, the answer there is to make a simple shell script that will append the proxy information to the file if it's not there, call it "debugchumby" and boot with it on a dongle.
If it gets screwed up, you should be able to restore the file to factory settings from the "Special Options" mode.
Anyway, details left as an exercise for the reader. Let us know how it turns out