On the note of Trivium 2 things: a) they did evolve during their career, so you might know a different trivium
b) they did evolve a lot during their career, so you gotta pick one where they actually played 7 strings. Ascendancy was 6 string drop D, Crusade I think has 7 and 6 string (mostly 7 if memory serves), Shogun is 7 string and with In Waves they went back to 6.
So mostly look at shogun stuff for 7 string, maybe some Crusade.
Personally I think they have just gotten better and better. Ascendancy was great, Crusade good (some really nice stuff in there), Shogun was pretty darn great and In Waves was bloody amazing, so many cool songs on there...the In Waves riff alone is so freaking cool.
Canīt wait for "Shark Sandwich".
Just learn Dream Theaters Dance of Eternity and I will give you a cookie! Great song for you, no singing =)
But really there is a lot of Dream Theater stuff that from a playing perspective is pretty darn amazing. Also great sweept parts for you in there!
Also early Fear Factory I think.
Additionally I think At the Gates played 6 strings in B standard, so that might be nice =) Old school Gothenburg meldic death.