Aha, I found the culprit. The configuration shown above lacks the configuration option vid. Adding
option vid '100'
and
option vid '200'
makes it work. Though I found I have flipped the order of the VLANs and have now settled on using 100 and 101 as the VLAN numbers.
So the bottom line of all this is: just don’t use VLAN numbers 1 and 2, and don’t forget to not only specify vlan, but also vid. That being said, to complete my understanding of the problem, can someone please explain the difference between the vlan and vid settings? And for completeness, what is the pvid setting mentioned in this thread I found by following the links?