Indeed, much remains to be done. I am already very happy with the semi-empirical formula I got for the average of the value of a set of pure short-range leaper with the same number of targets. I am inclined to interpret the formula as (30+5/8*N)*N, where the second factor (N) gives the direct effect of the moves (most likely through the capture aspect of it), while the 30+5/8*N describes the contribution of extra moves to the average mobility, which helps you to manouevre the piece in position to exert its attack.
My plan is to use the Lion as reference, and measure the contribution of each individual move (or pairs of moves related by lateral symmetry, as they should have identical contribution by symmetry arguments) to its value, by disabling them one at a time. Disabling a move will have a relatively small effect on the manouevrability, as the Lion has so many moves that it hardly suffers by missing one. But is should contribute proportionally to the second factor. So by measuring the drop in strength by disabling the move (by playing such a handicapped Lion against an unimpedent one), the second factor can be replaced by a sum of weights of all enabled moves, rather than just their total number. This way, each of the 14 possible move types can be assigned a weight. In fact I will measure the contributions of the capture and non-capture aspects of each move separately, and for the leaps will measure the effect of the leap being a 'lame' one, for capture and non-capture separately.
The captures will probably contribute almost nothing to the manouevrability, as Chess is not Pac-Man, and pieces are not manouevred in place by captures: the opponent will defend its pieces and recapture the first time we capture, so pieces usually do not survive their first capture. Unless it is a recapture itself, in which case we end up in a place by choice of the opponent, so usually not where we want to be. (Capture followed by 'recapture' on another square is far less common, as it is bad strategy to reply to a threat with a counter-threat,, as it gives the opponent the opportunituy to sac his threatened piece for anything of value.) So in a refined formula I expect the factor 30+5/8*N to be refined by replacing the N by a weigted sums over non-capture moves, while in the second term N will be replaced by a sum over capture moves.
It will take long enough to figure all that out, as there are 14 moves, whichhave to be tried as capture and non-capture, while 9 of them have also to be tested both ways in one or more lame versions. The double-Commoner you describe would furthermore introduce a kind of semi-lame moves, where a target an be reached through more than one lame path, so that the move can be blocked, but only by occupying several squares. (My guess is that such a move is practically as good as a direct leap.) And the lame Knight jumps are kid of double lame, as occupying one square can block two moves (of the Chinese Horse).
But after this project of disabling moves or move aspects one at the time in the Lion, whe should look how well certain special cases are predicted by the formula. I expect that for the weaker pieces (with only a small fraction of the Lion's move) the formula will not work, but will need some reduction factor for certain disadvantages that the moves it can do still have as a group. For instance, the Commoner is not merely an 8-target subset of the Lion, but a very special sub-set, where all distance-2 moves have been taken out. This is an especially detrimental combination of handicaps, as it reduces the speed of the piece. Similarly, taking away all color-changing moves will produce a global handicap of being color-bound, while taking away all color-conserving moves will cause some Zugzwang problems (the cause that KNNK is draw).
Another bad one would be to only allow moves in a certain direction, making the piece an irreversible one where every move would contract its 'event horizon' to cover a progressiely smaller part of the board. So I expect a piece that moves like the Pawn (but all moves capt+noncapt) to be far less valuable than a piece that moves diagonally forward and straight backward (fFbW), despite the fact that a forward move in general is worth much more than a backward move. So all these special conditions resulting from a fatal lack of cooperativity of the moves would have to be identified and quantified by measurements on the pieces that exhibit them.
And then I am not even talking about pieces that can do multiple captures in one move, or capture by jumping. These I don't consider proper Chess pieces, as one of the defining characteristics of a CV is that capture is made by replacement of the enemy piece on the target square. Checkers is not a CV! Fairy-Max does not support such pieces.
As this will be a very computationally intensive project, I am considering making a Joker80 derivative that supports other Leapers than Knight (plus a single King). Joker80 is far stroonger than Fairy-Max, and beats it at Gothic Chess even against a time odds of a factor 90. So it really would speed up things if I could use Joker80 to play the required matches. To achieve an accuracy of 1/10 of a Pawn (1.2% score) will require 1500 games…