I got it going. It was easier than I expected.
The strings came up missing for me as well but all I had to do was open up the BC304 string file, find the ones that were missing (e.g. ability names, descriptions and ship description) then adding them to the sg Galaxy string file. Works a treat.
EDIT: SanitySlayer's version makes the 304 a capital ship for the TEC and it fits in quite well.
I've just been playing a TEC vs wraith game and like in the show, just one 304 has a challenging time dealing with a hive ship (although things are made easier with Asgard Beams).
It makes sense to give it to the TEC though since they are essentially the SINS version of humanity.
There's nothing for it in the research tree since its available from the start, but I imagine that when the humans of Stargate get to mining asteroids and colonising planets, the 304 would already be a common vessel.
So far, I've had no minidumps with the combination of the two mods (Y).