A capture card might work - the fact that they're RCA implies that it's a straight analogue signal (A/V line in) so something has to either convert that to an RF signal (modulator) or an IP signal. A capture card might work for the latter, but you'd need to check; I don't think makemkv would do that, although you could do the same with an RCA output from a DVD or BluRay. I suspect HDCP would prevent full 1080p glory on the latter, though, but that might not be a problem for you.
VLC is pretty good at rebroadcasting, and there's still negge's proxy above. If you can capture the RCA stream in some way and store it to disc in the right format then either would potentially re-broadcast over IP in some way. At this point, I'm probably way beyond the point at which I'm making educated guesses and heading towards pure guesswork, though...!
