It should be possible to do that using one Ethernet port using VLANs. You could buy a cheap L2 managed switch and use it to trunk two different Ethernet networks on the same port. Then you would configure the Linux networking stack to split the VLANs into separate interfaces.
I am by no means a networking expert and was able to use technique to work around a similar issue in the past. It was easier than I expected!
SIGBOVIK is a parody of computer science conferences. It's a running joke hosted on April Fools Day every year at CMU - and apparently a quite convincing one. ;-)
Source: I attended SIGBOVIK a few times in grad school.
I am by no means a networking expert and was able to use technique to work around a similar issue in the past. It was easier than I expected!