I don't know how much use this info will be to you (you're in the US and I'm in Australia), but I have had very good dealings with a Chinese guy here in Sydney, who specialises in batteries, especially laptop batteries. He has a web site, but I have met him personally, and I found him to be very knowledgeable, indeed!
He can also get batteries "repacked," i.e., new cells put into them, which costs less (IIRC) than buying new batteries. (I'm not really exactly sure on that). He deals with another guy in Brisbane (that's about 500 miles north of Sydney, in another state), who specialises in repacking the batteries. It's not something you can do yourself unless you have the right skills.
A TP600 battery (I'm not sure if it's the same as a 600X battery) has four cells, each about double the length and thickness of a standard AA-size battery. They have to be hard-wired in a special way to a small circuit board inside the battery casing. It is that circuit board which regulates the charging process and tells the computer how much charge is remaining.
You could have a look at the laptop batteries web site and you can email him through his web-based email interface. His name is James Huang. I can't remember the name of the battery repacker in Brisbane, but I think he would probably tell you if you ask.
Even if it's not worthwhile for you to deal with an Australian company, (because of the distance involved), I think he would probably be able to point you towards a suitable dealer in the US.
Anyway, the website is:
http://www.laptopbattery.net.au/
Hope this helps. Good luck with it!