I have another idea...
What if, rather than always trying to balance the pieces, you split this into two Shogi variants. One with weak to medium-strength pieces and another with more powerful pieces? You can have a powerful piece in the former and a weak piece in the latter, but you wouldn't have to worry as much about finding the kind of balance you need now. The one with powerful pieces could be played on a longer board, since powerful tends to be synonymous with long-range in most cases.
What do you think? Do you want to keep just one single-dimensional variant, or do you want to experiment with two and split up the powerful and weaker pieces?