I know this is late for this year, and I DO NOT endorse this method. But it worked for me (so far).
I also live/work in NJ but have NY income and the 414(h) issue.
I cutoff the "h" from the box in my W2 and left it as just "414". It had no tax impact, I could e-file everything successfully, and I've received my refunds. If I'm ever audited or whatever, I figure this could easily just be a "typo".
