bp,
Polyurethane glue (your Gorilla Glue) is fine. It'll foam out so be prepared to clean up the joint line after a day or so. The new Titebond III will work just as well, stronger and is easier cleanup and no foaming. Either way is good though. Make yourself a tennon on one part and a mortise on the other so lining them up will be easier when you stick them together.
Another option, if you can arrange it, is to just make yourself a fixed tailstock 48" from your headstock. It can be as simple as just a 2x4 in a vice on a workbench that has a large nail pounded through it at the same height as the headstock drive center. For more ease of mounting and unmounting the woodturned piece your working on (not to mention a way to "tighten down" the tailstock center), you can substitute that nail with a bolt with it's end filed down to a point. Fit an appropriately sized nut in that 2x4 tailstock board and screw your bolt in and out of it.
What's that you say? What about actually turning that extra 12" that you don't have lathe bed (and can't get the toolrest to float in mid air to boot) for? Just turn the first 36" (actually more like 39" or more depending on how long your toolrest is); flip the piece end-for-end and work the remaining 12" (now) next to the headstock.
Just a few more options if you want,