Hmmm, I tried those formulae, but I get an invalid cell reference
error after substituting in the respective sheet names.

If I use

=SUMPRODUCT(COUNTIF(INDIRECT('Sheet 1'!H2&ROW(INDIRECT("1:16"))&"!
H2"),"W"))

the cell displays the correct number of W's, but obviously I want to
count across a number of sheets.