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...still...attempt to e-file them again using a zero for the prior year AGI. 

 

Many times, the prior year AGI for a mailed tax return doesn't get recorded in the E-file system, and you said you mailed them...so a zero might work.

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Maybe their procedures have changed, but in prior years, if you were forced to mail-file the state from the Desktop software after a rejection (or repeated rejections) they would refund/credit the state e-file fee. 

 

Maybe the person you talked to thought you were using the "Online" software...for that, they don't do a refund....but at least in prior years, the "desktop" state e-file fee was refundable/creditable.

____________*Answers are correct to the best of my knowledge when posted, but should not be considered to be legal or official tax advice.*