The idea of soloing group content on-level somewhat flies in the face of the concept of "group content". It means that there is solo content that is easy, and solo content that is difficult, but no actual group content.
On that score, I have had good success with a leveling group on Landroval. This is a group that uses the XP disabler to keep everybody on the same level so that, when group content comes up, they can form a group and do the content.
Even a single companion would be useful, and the XP disabler would mean you did not have to do EVERYTHING together. All you need is an agreement on your current level, and "we'll get together on Thursdays at 8:00 PM to team up for some of the more difficult stuff."
Currently, our leveling group is 27th level working out of Esteldin. We have completed the Book 3 fellowship quests as fellowship, travelled into the first level of Fornost, and ran several patrols through Dol Dinen and Nan Wathren in the past couple of weeks. When the characters reached 20th level and could enter the Great Barrow, we had the Great Barrow war - about 20 missions into the Great Barrow battling Sambrog and his minions. We have done several skirmishes, and the Erebor instances.
The short of it is that there has been little trouble getting a group together - a group of players at the appropriate level.
I also have a Moria group - but it is not a leveling group. It is level-locked at 60th level. But, when characters get to Moria and wish to do the Moria skirmishes and instances with an on-level group, there is a group waiting for them.
But, if you are still looking for a character that can solo group content, I should report that I have no trouble with either minstrel or warden - at least in the lower levels. Both have completed so-called "fellowship quests" 5 levels above the character level. The minstrel can kill just about anything too quickly for it to do any damage in return. The warden can heal its own wounds faster than those wounds can be inflicted on it.
Meadowlarke Sweetweed on Landroval. Also nephews and Bounders Ayrhawk, Wrennsong, and Little Meadowlark Sweetweed
Club Eclair roleplaying group on Landroval currently capped at Level 45 in eastern Angmar for all Shadows of Angmar end-game content (Alphred Troute, Hedgerow Shrewburrow).