This is a very interesting project, and I once made a similar attempt to extend the rating scale downwards, by analysing the results from the ChessWar promo division. One problem is that the weakest engines are often very unstable. And then they do not behave accordingly to the Elo curve, and analyzing their results as if they do, would extract wrong ratings. (E.g. there is an engine that prints "resign" in stead of "checkmate", so the weaker the opponent, the lower its average score against it.)
I tried to delete as many of obviously disturbing factors (e.g. games where a stronger engine crashed against a weaker one), but it is hard to catch everything. My conclusion (or rather, the result of the analysis) was that the rating of an engine like Pos 1.17 (in its non-random mode!) is slightly below zero, around -50 or so. And Pos 1.17 scores about 75% against a random mover.
The N-ply + random eval is sure to result in a nice set of stable engines that are asymptotically weak. It will take a chain of many of them before you will be able to connect to any decent rating. And connecting the random mover with the poule of decent engines by only one chain will be extremely unreliable. Connecting it through aother chain of engines might lead to a completely different rating. Nevertheless, the ratings of such N-ply random evaluators is of great fundamental interest.
I understood that Bob once did experiments like this. I am not sure about his implementation details. One question is how to evaluate a position where you are checkmated. Is that a normal evaluation, that you assign a random? Or do you assign it minus infinity. (It could be argued that that is cheating of some sort. Especially if you recognize stalemate seperately.) And would you play strictly by legal moves, or by King capture?
My engine NEG is very stable, and very weak, as it has no search. I especially made it to provide a stable engine in that Elo range. It just captures the piece with the best SEE, or if there is nothing to capture, tries a checking move. It does not know about checkmate. Nevertheless, it has won several games by checkmate in ChessWar. KQQQK is usually enough for it to accidentally win.
But it has also won through a kind of fool's mate.