In contrast, my inexact code is quite short=)
For a single open or closed die:
code:
//rolls a closed die, "sides" sides, numbered (low) to (low+sides-1)
private int rollDie(){return rand(sides)+low;}
//rolls an open die
private int rollDieOpen(){
face=total=rollDie();
while(face>=high){total+=(face=rollDie());}
return total;
}
//returns a random number, 0 to max-1
private int rand(int max){return (randy.nextInt()&mask)%max;}
Unfortunately, I do not know how slow the pseudorandomizer is, so I don't know how much avoiding it would help. I was considering pregenerating a lookup table that I could reference with a single random number, instead of multiple random numbers like 2d6*-2d6* simulation requires... but the table would be huge to be accurate. A table covering 99.999% of rolls would need 100,000 bytes, which would hurt Cache performance. Alternately, storing the probability table you provided and looking up the value would require minimum n(log(n)) steps to look up a roll from a probability.
A single formula, in this form:
code:
int convertTo2d6roll(double probability){
return something;
}
...assuming the code was fairly short...
...would speed up things a lot.
Of course, the ultimate distribution would still be entirely dependant on Java's pseudorandomizer 
However, from examining what you wrote below, which I do not very much understand (but I think I should if I remembered my stats class)... it looks like it has a lot of expensive double-precision floating point division.
Regardless of speed, I would love to see code that implements it, if you have time! And I'll try to figure out what you wrote below, tomorrow=)
-Cherry
P.S. To post code on these forums: Use ["code"] blah blah ["/code"] format. Without the quotes 