Try leaving the number space entirely blank at first. If there is any issue with Box 15 that prevents e-filing your return with a blank Box 15, and it absolutely requires some value in the software, then either try using the payer's Federal EIN again here, or enter a "nonsense" value such as 12345 67890 (with a space in the middle, or not).
The State ID is a bureaucratic convention for your state; the state can and will still be able to easily and uniquely identify your employer by their federal EIN, even if they have to cross-reference the Federal / State ID numbers in their database. In other words, this single issue should not affect the processing of your tax return, as long as you can satisfy the software with some acceptable input (or none at all).