That's probably 'Deep Ellum,' the red-light district of Dallas (from 'Deep Elm', though I don't know the derivation of 'Ellum' other than mispronunciation).

Alas, the only song I know about it is 'Deep Ellum Blues,' which doesn't sound at all like 'Move It On Over.'

Deep Ellum Blues

If you go down to Deep Ellum, keep your money in your pants,
'Cause those women in Deep Ellum won't give a man a chance.

Refrain: Oh, sweet mama, Daddy's got them Deep Ellum Blues. (2X)

If you go down to Deep Ellum, keep your money in your socks,
'Cause those women in Deep Ellum will run you on the rocks.

Refrain

Once I knew a preacher, preached the Bible through and through,
He went down to Deep Ellum, now his Bible days are through.

Refrain

... if this sounds like the phraseology of the song you heard, I don't see how it could sound like "Move It ..."

Just my opinion.

Bob