I put He Man in the same ballpark as classic Sasquatch (when he was being given great showings), slightly above Thing, She Hulk, etc. and right around Wonder Man/Ulik level. I also consider Wonder Woman in this ballpark.
She Ra moved a moon, not sure when He Man did, but I also think He Man is a little stronger than She Ra.
He also struggled to overpower Clawful and others, who in turn struggled with human levellers like Teela.
Yes, he did well against Pre Crisis Superman, but there are multiple versions of the character, the old Star comics version, the cartoon, the modern comics version, and the DC miniseries and crossovers.
All in all, I don't see enough evidence putting him on the true top tier list, but enough putting him on the next tier down. I think Abomination would be measurably and demonstrably stronger, but not overwhelmingly so, and I think He Man's brains and skill would have him beat Abomination, even without using his sword.