You'd be surprised what people are willing to run, sometimes. A lot of players have multiple alts and such, or else are willing to run their mains through under-level content for deeds or (especially) relics. So, feel free to ask around in your server's GLFF or even the local LFF channel for wherever you are.
Moria instances are especially popular for dropping a ton of relics that can be either combined or deconstructed for shards.
But, your best bet for finding groups not only at mid-level but even once you reach end game (which will happen, unlikely as it seems when you're level 42!) is to find a kinship.
[b][SIZE=3][COLOR="#FFFFFF"]Cainwen Ciaphas[/COLOR][/SIZE][/b][COLOR="#C3C3C3"], Captain of Crickhollow, [url=http://tvtropes.org/pmwiki/pmwiki.php/Literature/CiaphasCain]HERO OF MIDDLE EARTH[/url]!!!
[i]I will not be pushed, filed, stamped, indexed, briefed, debriefed, or numbered![/i] My opinions are my own![/color]