What about the Papilio Pro?
" The Papilio Pro (Spartan 6) has direct TMDS I/O support which means that DVI and HDMI interfaces can be implemented without any extra chips. "
It's the speed and electrical signal standard that determines if HDMI is possible. RocketPort should be sufficient.
Xilinx Spartan 6 - probably has enough capacity.
Again hard data lacks..
(specific chip and package, specific Mbit/s rate, specific electrical standard etc)
DVI is completely free to implement (asfaik). With HDMI there's even a fee on having the chip mounted or the specific connector.