Has anyone here ever owed money to the military and negotiated
a reduced debt?

I was accused of owing $2000 once. I found out when I went to my
post office box in Iceland and noted that my pay check was for $ 0.00
which is pretty neat, and I have it framed. (pre-direct deposit days)

After going to Navy Accounting & Finance, I found out that my pay records
were so screwed-up, that Langley AFB Finance had to intervene on my
behalf.

No option of negotiated settlement was offered :-)

I did finally get it fixed, and payed at the cashiers window.