I think Eric has got you on the right track to get you going on your current setup.

I did want to share a few other options that I've found while researching for myself:

1) Memory Capacitor.
(This one eliminates the batteries all together. Won't keep score if powered off for a long period of time.)

I just picked up a BH on 2/7. I checked to make sure the old DataSentry battery was removed. It was and had one of these memory capacitors applied in its place.
https://www.greatplainselectronics.com
Part number: CERS-1.5F-5V

Some video I found:

2) anypin NVRAM.
(this one also eliminates the batteries all together. Also a good option if your 5101 is indeed bad.)

http://lockwhenlit.com/anyPin.htm
they have a 5101 version that is a bit cheaper.

Some video:

skip ahead to 4:00~4:35

3) CR2032 coin battery and standard holder.
This option puts a battery back on the board. So, maybe not the best option. It also needs a diode, but I'm not sure how the diode should be installed. Anybody have instructions on how to install the CR2032 battery option?

I also have a MGOW. Not sure which method I will use for "battery" backup, but I just had to get that old DataSentry battery off of there. Luckily, no damage was done.