Monte Carlo estimation of the Hypergeometric Function
I am the Adams of Adams-Skopek.  I want to point out a couple of things:


You get some truncation error when you sum or multiply a series of values in different orders.  You need to estimate this and account for it.
There is a lower limit on sparsity of the data, you need to address this.
If you can get a copy of the Pagano and Halverson program (cited in Adams and Skopek), it is useful for comparing it's results with your results.   It does the exact hypergeometric test very efficiently.
There is a PC version here. You might need to ask the authors for the code.
The computer department here can probably locate the original Fortran code for the original version of the Adams Skopek program and give you a copy (which I don't have).