Thanks for the excellent feedback!
The 9V alkaline battery died Sunday, so I've just replaced it again. I measured the old battery at 5.5V!! So it well and truly used it up. I needed to continue data logging ASAP, so I opted for a f#% expensive 9V lithium primary ($16 from Altronics!!)
...I was desperate. Anyway, that should keep it running for at least another week. So I have time to implement something better.
To answer a few questions. A bench-top unit may be an option, but I'll be bigger/bulkier, and cost me a bit. I'm happy with the Protek 608 performance so a cheap mod will be ideal.
The battery compartment has it's own door and compartment, so a DC-DC module to fit in there looks like the ticket. I would like to have a DC jack on the door so everything is nicely sealed. Then I could plug in a 6xAA battery pack or wall-wart.
I'm halfway through building a 3D printer, so soon I could even make a custom door and not have to drill a hole in the original door. I will connect the DC-DC converter to the DMM with it's existing 9V battery snap. This way I can remove my mods, and nothing is permanent.
I've attached a couple of photos of the battery bay.