You should certainly aim for Mordred ASAP. And pick up Gawain if you haven't already. Dartagnan is good to have, but Mordred gives you Black Propaganda which is extremely important.

Sol would be extremely good for you, yes. Your Thunder team still won't be strong since you'll be missing debuffs, that's something that Thunder lacks until... third Miracle ticket? Is Mammon available on the third one?
Anyway, with Sol and two off-core Thunder SSRs, it will still make a decent team... and Sol would benefit all your groups.

You will probably want to read Sanahtlig's team building guide though. In case you want to start building some more recommended elements than Thunder or Light already.