Corded Andis BGRC to battery power?

Woops. That about sums up what I've learned about turning a corded Andis BGRC into a battery powered hair clipper.

Andis BGRC: Great Clipper
Anyway, I love my Andis BGRC for shaving my own head. In the past few years, I have used the Oster Classic 76, Oster Fast Feed, some $20 hair clippers, and the BGRC. Each one, aside from the cheap units that I got sick of quickly, were used for around a year each at twice a week. Only the BGRC hasn't given me a major itch to upgrade unless you count my desire for it to be cordless.

Andis BGRC, BGR+, and BGRV
Let's start with a bit of background information. The Andis BGR series comes in at least three flavors:

Andis BGRC Hair Clipper
Andis BGR+ Rechargeable Cordless Hair Clippers
Andis BGRV Variable Speed Hair Clipper

When I decided to get my BGRC, the only other model that interested me was the BGR+ for the cordless feature. However, the price difference was about $100 between them. There was no desire to have a battery powered device at the time because I had gotten so used to corded clippers. That has obviously changed, but I'm now wishing that I splurged early on.

Andis BGRC Unboxed

Turning a corded BGRC into a cordless clipper?
Before I pulled the trigger on buying my BGRC, I was aware that it should have been possible to upgrade to cordless at anytime by buying the battery and charger. I just didn't know which and for how much. After doing some research, it appears that it would have been cheaper to buy the BGR+ and downgrade to a corded clipper than to upgrade from a BGRC.

This is all assuming that I have found the right parts though. Without buying the charger and battery pack to test it out, which I've yet to do, there's no way for me to confirm if they work or not. Something to keep in mind while reading this...

So what parts do I think are required to turn a BGRC cordless?

1. Andis 64725 Power Pack Rechargeable Battery
2. Andis Sensa Charge Replacement Charging System 64720

At the time of writing, the battery was listed for about US$ 50 and the charger for US$ 85. That is a total of US$ 135. Where's the problem? Here, if it's the right unit:

Andis 63070 Cord Pack Adapter

Again, at the time of writing, the cost of the BGRC was about US$ 110, the BGR+ was US$ 200, and the cord pack was US$ 30. If all the parts fit together like I think, then the cost of having roughly the same parts (i.e. cord, battery, charger, and clipper) would be US$ 245 starting from the BGRC and US$ 230 starting from the BGR+. However, I doubt that I would get a cord pack for the BGR+ unless absolutely necessary (i.e. something broke or I started a barber shop) or the battery turned out to be a dud. This really is the big one because the US$ 15 difference isn't that big, but US$ 45 (US$ 15 difference plus $US$ 30 for the cord pack) is.


Related
Andis BGRC Hair Clipper Review: First Impressions
Andis BGRC Hair Clipper Review: Second Impressions
Oster Fast Feed and Classic 76 Review