I uploaded GoL.js and GoL.html. They don't "work" yet but they allowed me to test the following, functional code:

    L2=world[i];
    L1=world[i-1];
    L3=world[i+1];

    // half adder:
    S20 = L1 ^ L3;
    S21 = L1 & L3;
    // full adder:
    S31 = L1 | L3;
    S30 = S20 ^ L2;
    S31 = S31 & L2;
    S31 = S31 | S21;

    // Sum LSB
    S0 = (S30>>>1) ^ S20;
    S0 = (S30<< 1) ^ S0;

    // LSB Carry
    S0C = (S30<< 1) | S20;
    S20_= (S30<< 1) & S20;
    S0C = (S30>>>1) & S0C;
    S0C = S0C | S20_;

    // Sum middle bit
    S1 = S31>>>1 ^ S0C;
    S1 = S31<<1  ^ S1;
    S1 = S21     ^ S1;

// Inhibit
    INH = S31<<1 & S21;
    S1_ = S31<<1 ^ S21;
    C2 = S31>>1 & S0C;
    INH = INH | C2;
    S2_ = S31>>1 ^ S0C;
    S2_ = S2_ & S1_;
    INH = INH | S2_;

    X2 = S0 | L2;
    X2 = X2 & S1;
    X2 = X2 & ~INH; // The result is now in X2

This is the contents of the inner computational loop, made of a series of half-adder and full-adder "blocks" that perform the bit 2D counting (popcount). This will evolve, as well as the surrounding code, to keep the number of needed registers as low as possible (4 for AMBAP, plus 2 mapped to memory).