I don't see any way to handle the market discount correctly for New Jersey in the TurboTax interview. That means it's one of the many things that can only be entered in forms mode. Since there is no forms mode in TurboTax Online, it requires using the CD/Download Desktop TurboTax software rather than TurboTax Online.
In the desktop software you just put an X in the Tax-Exempt box for the market discount amount on the New Jersey Interest and Dividend Income Worksheet, and that takes care of it.
I'm not sure that your idea of fudging a 1099-INT would work at all, or produce the correct results. If it does work, it might not cause a problem with the IRS if you do not have Schedule B in your tax return. But if you do have Schedule B there would be an obvious mismatch between the 1099-INT and what is reported on Schedule B. In that case I expect that you would get a notice from the IRS saying that you underreported interest income.
Be careful with the word "override." In TurboTax an override means forcing a change of a result that TurboTax calculated. An override can cause the automatic calculations to break in unexpected ways, even in places that you think are not related to the override. An override cancels the accuracy guarantee and also prevents e-filing. Overrides must be avoided except in very unusual circumstances. What you want to do, putting an X in a box on a worksheet, is not an override. It's just an entry on a form.
