Rubilia/ Environmental No Pass Go

Environmental Go as described at http://www.britgo.org/results/env/, using area (or territory) scoring, ends when the last coupon has been taken and all worthwhile board plays have been made. For "environmental no pass go'', I'd like to attach the environment to No-pass Go rather than to usual Go, and place the stack of coupons ranging from somewhere around "boardsize moku" down to "(Z+1/2) moku" on top of an infinite pile of "Z moku" coupons. As far as I can see, for 0, the resulting board game would be the same, upto the point where the game of environmental go ends.

What happens if the value of the infinite tail is set to another integer Z, though? With such a generalization, as long as some superko rule prevents the board position from cycling, the game ends up alternating between two scores Z moku apart. Play may stop, with the final score being set to the average of those two, as soon as neither the board nor the pile of coupons is altered by two consecutive moves.

If Y0 is the minimum move value available under a certain scoring method, then Y0 should be recognizable as the least upper bound of Z such that the board game remains unchanged for all Z <= Y0.

(For Z >= 0, the game depends on whether "unfinished" positions are scored according to actual scores or mean scores. The latter sounds more reasonable but may require hypothetical evaluation and hence be not practical in many cases. Anyway, all positions will be played out (in the common Go sense) before a negative coupon is taken, so the problem vanishes for Z < 0.)

In CGT, the temperature is never smaller than than -1 moku. However, I tend to believe that, in environmental no pass go with area scoring, Y0 is smaller than 0, and with territory scoring, Y0 is smaller than -1 (game start being the (sufficiently large) empty board).