I did make a battery, but I haven't installed it yet, aside from putting it in once to test. The maximum float charge on the battery is 13.8V, but the stock Miata alternator puts out 14.0-14.5V. It might be okay to put it in as is, but to be safe I need to drop the voltage coming out of the alternator by almost a volt.
I bought another used Miata alternator in the hopes of modifying the voltage regulator, but it uses an IC regulator, so I might not be able to do it. I'm planning to play around with it this weekend and see if I can get something to work without too much trouble.
For anyone who is interested, the battery I made contains 12 A123 Systems lithium iron phosphate cells. It has 360A peak current output, and is 6.9Ah. The total weight including my waterproof enclosure is just under 3.5 pounds.
http://www.msu.edu/%7Eushernat/IMG_0056.JPG