Another solver to take a look at is MAXIMA (a relative of MACSYMA). I have used this going in the other direction, where I have a set of equations and I want to turn the solution of these equations into a spreadsheet, where I can type in the knowns to find the unknowns.

Your problems is difficult, since you have presumably working spreadsheets, and any other given solver may or may not be able to converge on the same solution. It might be a good idea to find a few problems that they weren't able to solve in Excell and see if any solver that you come up with can do better.

The advantage of a computer algebra system such as MAXIMA is that it can come up with a closed-form solution, so no iterations are necessary. The disadvantage is that it may not solve the problem, where an iterating approach could.

It should work perfectly the first time! - toma