George Milburn was the author/collector of The Hobo's Hornbook: A Repertory for a Gutter Jongleur (1930), which I think is much too early for this song. Copies are rare and expensive: the last one I saw listed was $275. Ed Cray (EROTIC MUSE) would be the guy to ask if this song is in it - I'm sure he's got a copy.

I believe the hero is "slingin' (not "swingin') rigging". This looks like a gyppo (cheap – haywire – dangerous – non-union) outfit where one guy is both rigging slinger and hooker.

A rigging slinger directs his choke setters or chokermen in high lead, slack line, or similar log yarding systems. The chokermen loop 16' cables or chokers around logs felled and waiting to be yarded. The rigging slinger determines the sequence of logs to be yarded, according to guidelines established by hook tender (or hooker). He issues directions to crew regarding which logs are to be yarded, the positioning and securing of chokers, and the position of crew during the movement of logs. These days, he signals the yarding engineer (or donkey puncher) to control the positioning of choker cables using a portable radio. In earlier days, he signaled to the whistle-punk (who held a wire connected back to the steam whistle on the donkey engine or skidder) who blew a series of whistles)). He has a bunch of other responsibilities, too, including training new chokermen.

And his girlfriend, Molly Hogan?

A Molly Hogan is a typical haywire fix-it for a lost cotter pin or the like. Here's how Tom Parkin defines it in Wet Coast Words (though I kinda doubt his etymology):

In logging, a wire strand, cut from a cable, used as a cotter pin. Canada. A Molly Hogan is a strand of wire pushed through a hole and twisted in place. It is used to replace a cotter pin which is easily lost in the bush. The word developed from Molle – fr for "soft".

I've not heard the song before, though I'd say it's more likely a newer song (80's?). There was a group in Oregon called Timberbound: I think the names were John & Kim Cunick. That might be a place to start. There's also a thesis from Florida on northwest coast logging songs by Leslie Johnson. A fascinating read by itself, but her bibliography might provide some useful leads. I don't think the song comes from our side of the line.

Jon Bartlett