I tried to calculate rough estimates for the values of the pieces, using the Safe Check principle. This is, simply put, if you place a piece and a King randomly on the board, the probability of that piece giving a 'safe check' to the King. For pieces like the Knight this like the movement estimation.
[[ The following calculations assume that the Querquisite on the e-file moves like a King, but the one on the D-file moves like a Queen. Any changes in the definitions of files (as in Fischer Random) might change the value of the Querquisite. ]]
I came out with these percentages :
R= 15.7 %
B= 8.7 %
N= 7.9 %
U= 10.8 %
And the Queen is simply the sum of its components. So are the Chancellor (Rook+Knight) and Archbishop (Bishop+Knight.) The Querquisite's compounds are a waste of time to calculate, since they're not practical.
Giving the Knight the absolute value of 3 Pawns, these are the values:
N= 3 Pawns
B= 3.3 Pawns
R= 6 Pawns (However, as in normal Chess, I think they should be
adjusted to 5 Pawns.)
Q= 9.4 Pawns
U= 4 Pawns
Out of curiosity, I computed the two Capablanca pieces on this board:
A= 6.3 Pawns
C= 9.4 Pawns
This seems about right. It's worth mentioning that the values would certainly change on a 10x8 board with these two Half-Ranks added.
The Querquisite, generally, is most mobile on the Rooks and Queen's files. Place it there.