It's actually kind of interesting how things have turned out. I think the guild leadership expected to be a casual Normal-mode guild for the most part, and maybe work on a few heroic bosses in the time left after the Normal raid ended. So we've ended up with a Normal raid on Friday where everyone in the guild is welcome to come. And then we have a Heroic raid on Saturday which you have to "qualify" for.
The qualifications are really low, but it's just enough that you actually know the correct rotation for your spec and have minimal gear. But it's kind of indicative of the mindset of the guild, in that they see Heroic as "not for casuals".
The problem, however, is that even though we raid two days a week, it's sort of like we only raid one day a week, but in two different worlds. Friday we do 7/7 N EN, and there's maybe enough time to poke at Odyn. Saturday is 7/7 H EN, and again, barely enough time to poke at Trials of Valor.
If you add to that the casual inclination to farm gear before tackling something hard, and you can see how--even though we are relatively successful--we're kind of stuck at the same time, and not really progressing forward.
To me, the best solution would be to see if we can take the Friday group to Heroic EN. The vast majority of the raid is the same for both nights. (Though a lot of people now play alts on Friday.) If we can kill 3 or 4 Heroic bosses on Friday, I think that would free up enough time on Saturday to make solid attempts on Trials of Valor.
But I don't know if that squares with the way guild leadership views Heroic raiding. Ultimately, in their heart of hearts, I think they still believe we are a Normal mode guild, and the majority of people in the guild aren't really ready for Heroic raiding.