I thought about this as a simple mutator (as you call it) on your initial idea of adding on a capablanca board minor pieces and as I'm uncomfortable with the modern elephant for being color bound I replaced it with the Spartan lieutenant. The waffle/phoenix and the frog seem like natural additions.

An difficulty I have with these ideas is that the frog's trebuchet jump may be a bit too much :)!

But then something HG once said to me in the context of discussions about apothecary chess 2 (correctly I think) is that you need more strong pieces to make the game a bit faster and more decisive. I'd propose, in order to make the exchanges more interesting to have pieces close to queen value. So I propose for the added major piece besides, the minor ones I've considered above: the Marshall (R+N), the Minister (B+N+W)- there are probably other names for this one- and the unicorn (B+NN)- the strongest of the three. For which is with which I though to pair the game with Spartan Lieutenants with the Marshals (in order to have a diagonal and orthogonal piece), the game with the waffle/phoenix with the Unicorn (as there the unicorn is the only strong piece proposed with no wazir move) and the frog game will have the Minister. But I would not add a new strong piece in the normal setup by expanding the capablanca board or pushing or deleting pawns. But through an alternative piece introduction method. This would be other gating (the piece sits behind a friendly piece and takes it's place when this one got moved), the Seiwaran way, or through bruhaha squares. Out of those here I'd prefer gating as the Seiwaran way leads to sometimes game-breaking tactics and the Bruhaha way is to fixed. Gating would alleviate a bit of the first move advantage as black would be able to create his strategy already knowing where the white gated piece goes.

Next are some diagrams illustrating what I think maybe it's good to be considered:

 

 

Thinking about the initial setups was not trivial and quite fun so I'm glad the best turned to be different. I chose reasonable gating options to be displayed by both players.

And the most important thing, although I think Kevin you are not quite comfortable with this one. But I'm putting it out there for discursion.  I almost always though that practical promotion only to queen is maybe not such a good idea. So I think I/we should consider 7th rank promotion to lesser pieces.  The question here is "to rook or not to rook"!... Well, if we allow promotion to rook than most promotion will be rook as basically you will never promote at 7th rank to non-rook and it really rare to promote to the stronger pieces as an extra rook (almost, you do lose your promoting pawn after all)  usually wins you the game among serious players. The second alternative is to promote to any of the 3 minor pieces but not rook. That is quite good actually as the 3 minor pieces are close in value and there are plenty of opportunities to promote the the slightly weaker ones. But then there will be no promotion to rook, and personally I don't like that just for it and besides now KP vs K is again not necessarily a win as it would be when being able to promote to a rook on the 7th rank. So I had cooked a third longer but I'm thinking better rule.

A player can promote a pawn to a rook on the 7th rank if at least one of the two following cases occurs

1. The next two conditions are both simultaneously true:

  i). This player has already promoted another pawn regardless of to which it had promoted it

  ii). This player has at least double the number of all minor pieces to the number of rooks

2. The player is down to it's last pawn

Kevin besides maybe other concerns I think you are thinking that this rule is to complex for new players. But I don't think this is a big issue as player will come in contact with this rule later anyway, after getting the basic differences. But I do think that it makes the game have more options :), and that tends to be good :)!