I didn't even take the time to go through the examples, but agree with payrollguy and cbg. The employer's payroll system will do the correct calculations for taxes/deferrals and won't double anything. There might be some weird "innies" and "outies" on the paystubs, but in the end, it will wash. On the off chance that you get more federal/state income tax withheld, it will be returned in your personal tax calculations at the end of the year. (and it is possible in some systems that it will equal out if they do any ytd tax calculations)

In the end if the union is unwilling to help, it means there's nothing to fight. Employers change pay systems and methods. That is very legal. And the fact that they are offering an advance is generous. They do not legally have to do so (unless the CBA requires it of course)