So I did some tests with some 800mAH 14500 Li-ion batteries. 3 of them in parallel is roughly equivalent to 3 NiMH cells in series. I did a comparison of battery life, and the NiMH cells lasted about 8.5 hours, and the Li-ion cells lasted about 9.75 hours. The performance benefit is there, but probably not worth the hassle of coverting the scanner to use them.
I've changed my mind about this. Either I didn't have the Li-ion cells fully charged in the previous test, or else they needed a few charge/discharge cycles to reach full capacity. Also, the charger board was also generating a little RFI that was making the 436 low voltage cutoff trip multiple times, starting at about 3.5V.
For this test, I put a 0.1μF capacitor across the output terminals of the charger board, and had the battery plugged in to the charger board overnight before starting the test. With the display backlight off, volume set to 8, the same favorite list as the previous tests, battery saver turned on, and GPS turned off, I got a run time of
13:35:34 from the time I unplugged USB to getting the low battery warning. I was able to plug in to USB power before the scanner shut down.
3100mV is a decent setting for low voltage. The cells are over 99% depleted at that point.
I made a cutout in the case so that the USB jack on the charger board can be used. This has the advantage of allowing the charge status lights on the board to be visible, and also allows you to plug in to USB power without any annoying menu prompts.
https://1drv.ms/u/s!ApJIS-l4xqPtguo5H7IjxIZbZ-eZng
To get the board to fit properly, I created a template and milled out pockets for the chips and other components on the board, as well as the USB jack. Here's a photo of the board snugly fit into a piece of scrap plexiglas I used as a test before hacking the scanner case.
https://1drv.ms/u/s!ApJIS-l4xqPtguofCT5ANZPFQBmHug
The pockets for the board and components had to be milled from the inside, but the cutout for the USB plug had to be milled from the outside. So I had to use the middle-left case screw hole as a zero reference so I cut in the same place from both sides.
The cells I'm using are 800mAH Tenergy Li-ion 14500s with solder tabs:
https://www.amazon.com/gp/product/B003EWA5Z6/
I removed the battery terminals on the scanner front circuit board. I used 3-pin 1.25mm JST connectors to connect the battery to the charger board, and the charger board to the front circuit board.