Rate Start: First of Pay Period Preceding First Check On/After Coverage Start?

I'm having trouble with writing a fast formula for a rate start code using logic like 'First of Pay Period Preceding First Check On/After Event' but instead of using the event date we need to use the coverage start date - has anyone used a similar one?

The business rule for the Virginia Retirement System is that employees hired or having salary changes that happen on the first day of the current month or from the 2nd->final day of previous month, get their service credit in the current month.  And we must take the increased deduction/employer costing starting on the first check of that month (we process biweekly payroll).  So the contributions we deduct in the month are based on salary as of the first day of the current month.