Breakthrough!
I managed to dump the SA-1 cart. I actually dumped PGA Tour 96 yesterday before my previous post. I was going to include the news in that post but since I only had only managed it once (I finished the hardware addition that same day), I deleted the details before posting. I managed to dump the same cart again today and verified the contents of the ROM which appears to be a previously undumped version of the game. My ROM and SRAM dump both work in higan although I haven't played thru a game yet.
Dumping the SA-1 cart requires attaching a CIC chip in lock configuration. I built two different versions of the CIC lock - one using a SuperCIC 16F630 and one with a snesCIC 12F629. I've dumped the PGA Tour 96 using both versions. The cart connector CIC pins (24, 25, 55, 56) need to be connected to the CIC lock chip. Pin 56 is connected to the CIC chip and a 3.072MHz clock signal (I'm using one of the other clock outputs from the Adafruit Clock Generator).
The CIC-SA1 connection is a bit hit-or-miss right now. Most of the time it doesn't connect but it will eventually work. I think I have to tweak the reset timings to get it working more consistently. What was amazing is that I managed to dump Super Mario RPG on the first attempt using the SuperCIC. It was nice to finally get a copy of my savegame off the cart. Kirby Super Star dumped on the first attempt with the snesCIC. Kirby's Dream Land 3 dumped ok but is giving inconsistent SRAM dumps so I suspect the battery might be dying.
Another good thing about the CIC addition is that it works fine with the other non-SA1 carts. There is one cart that does need to have the CIC module removed and it is the Nintendo Power (SF Memory Cassette). With the CIC module connected, the Nintendo Power cart won't be recognized by the reader. I'm assuming the CIC module and the MX15001TFC processor chip don't get along. I'll have to do more testing to see if there is a workaround.
EDIT: The changes to the setup() code with the CIC Lock Reset outlined below have fixed the issue with the one problematic Nintendo Power cart.
I'll post more details after further testing.