Hello,
In response to your battery question:
Looking for a datasheet, I found a source Here .
The only conclusion is that I would strongly advise aginst it!
These are standard Lithium-Ion chemistry, which means that they are charged at 4.2V. So a fresh battery will expose your calculator to a little less than 4.2V, and will only decrease to a safer level of around 3.6V after having used 80% of its capacity (see figs. 7.1 & 7.2). I believe there is a strong risk of damaging your calculator, even after only a single try.
Moreover, to protect the LIR batteries against overdischarge, you would have to monitor "manually" their voltage quite regularly and take them out of the calc as soon as they reach 3V. Note that this is nearly the fresh voltage of a CR2032, so the software will not warn you at that point. Overdischarging these cells will ruin them very fast, and might even be a real hazard.
You can also see that their capacity is quite modest (approx. 1/6 of the CR2032).
OTOH, they woud not suffer from the 20mA load from the calculator.
I would like to see what would be achievable with an LiFePO technology. That should be voltage-compatible, but might offer an even slightly lower capacity.
Regards,
Etienne
[edit] clarifications
Edited: 28 Sept 2011, 7:13 a.m. after one or more responses were posted