Sometimes you just gotta suck it up, wait for groups, and griiiiind it out.
Something that really helps is actually talking to people -- don't just /ooc at the zoneline and expect people to send you tells. Get an invis and actually walks up to the group you'd like to join and send specific people tells, ask who the group leader (GL) is. I've often gotten spots in groups because people didn't necessarily want my particular class in their group enough to send *me* a tell, but when I was there "in person" they just decided to say fuck it and shoot me an invite.
If that doesn't work, ask the GL to put you on the list and then log over to one of your other characters -- keep in touch with the GL from your alt, checking in with a tell every so often.
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