Open Forum

The second will probably involve a "process" adjustment in your payroll.  Most companies have a matching "company paid" deduction setup for the 401K match or an amount is simply determined by the company to add to the employee's plan.  Either way, this amount should be added as an earnings type and only specify the IL tax deductions in the Deduction listing and it will NOT contribute to net pay and IS excluded from disposable earnings.  When the employer contribution is determined, it will need to be added under that Earnings Type in Time and Dollar.  This will take care of the employees check.
You will need to contact the manager of the plan because if you have the calculation done at the time of the payroll calculation and it is not an arbitrary amount, you will need to calculate, get the amount for the match, uncalculate the payroll, enter the contribution in Time and Dollar, then recalculate (what a mess).  Or, if your plan allows, this amount could be calculated and added to the employee's next check.  Most contributions simply must be submitted but it would probably be OK to add to the employee's check calculation in the next pay period much like you would add additional life insurance premium earnings.

There is still one more issue.  I am not sure if not associating the employer's contribution with a Federal Tax (FED1, FED2, etc.) would actually exclude the earnings from the W2 if it is a "Regular" earnings type.  That is something you could test by running a W2 calculation in a test environment after the process is put in place.

Maybe another issue also in that most exclusions for SUTA also follow the state tax laws so may want to pay attention to that also.

I do like Michael's idea of relocation.  Could open a small headquarters office in St. Louis, only 2 hours away.  I am sure if this works for IL other states will follow since their all broke and need more tax money.