I recently saw a Punch Brothers show and Paul Kowert repeated a short lick an octave higher and higher until the pitch was higher than I ever thought a double/upright bass could go. He was definitely off the fingerboard, and may have been playing behind the bridge, but I don't quite remember. At any rate, are there positions after the fingerboard comes to an end and/or behind the bridge? If so, how might I refer to them? I unfortunately have no experience with fretless instruments and have pretty much exhausted all the search keywords I can think of. Currently surfing YouTube in search of high bass notes via pinched strings...
No, there are no formal positions behind the bridge.
As a double bassist myself, what I believe you are looking for is this: (v)
The Simandl method just would describe that positon as thumb positon but the Rabbath method would describe it as 6th postion.