If you place the current sheet name in a cell, like putting bizB in cell D3 (for example), then your formula can be =INDIRECT("'C:\[FormulaFile.xls]" & D3 & "'!A20)
which will work fine with one caveat -- for it to calculate correctly, that file MUST be open, or you'll get a #REF! error.
Alternatively a macro can also work that shouldn't be too difficult.
If you need a starter, try recording what you'd have to change.
for example do a global replace of "bizA" with "bizB".