As a precision reference, here's the 1e5/2e5 answer computed with my program. It ought to be good for 60 digits:

[thor@redwood fishers-exact-test]$ cat fetbig.dat
100000 200000
200000 100000

[thor@redwood fishers-exact-test]$ time ./fet <fetbig.dat
+1.324994596496999433060120009448386330459655228210366819887079e-14760
real    21m8.445s
user    20m56.788s
sys     0m6.831s
[download]

It looks like your FET6 yields about 13 digits of precision for this case:

               |
 1.32499459649680040e-14760
+1.324994596496999433060120009448386330459655228210366819887079e-14760
               |
[download]