I have no idea whether this is relevant, but I found this in an "EXCERPT FROM TRANSCRIPT OF MEETING WITH
THE ASSISTANT SECRETARY OF AGRICULTURE FOR CIVIL RIGHTS.
SEPTEMBER 18, 2003":
Now, those employees f or four years have been sitting in limbo with EEO complaints, working in hostile environments in places like Gump Stump, Mississippi Not only are they being hurt economically and socially, I have been in contact with these employees and there is also a physical danger involved. Its not like they are working in Vallejo or Washington D.C., they are in some very remote areas.

And, there's a song called "Opossom Up A Gump Stump" and one called "Rabbit up a gump stump"; hmm--given that plus the ref. to MS, I wonder if the song refers to a gumbo tree.

Here's a quote from a school site that sounds like it has your meaning, bev--welcome aBoard, by the way: We have coordinators, facilitators, special this and special that, up the gump stump.

I also found this quote: If it wasn't for Social Security, I'd be up a gump stump.” And this one:I've been licensed, tenured and degreed up the gump stump.

So, apparently the phrase has at least two meanings: 1.) a whole lot, and 2.) in trouble. Wow--if you find the REAL origin, do post it, please!