FYI ... after you have rolled the 403B to an IRA then you can convert some or all to the ROTH ... since you have little to no income it would be a tax benefit ... or, if the 403b allows it, you could roll it directly to the ROTH.  Seek assistance from the 403b & IRA custodians to see what your options are and from a financial advisor/tax preparer to see what this may do for you.  But be quick you only have a few days to get this done for 2017.

Ok, thank you both!

I called my custodian and they said the conversion would count as income for the year. If I made no income, but move $7,000 into the Roth, I am still below the poverty line as a single adult with no dependents. I may have to pay 10% tax on this unless I qualify for some other credits.

You don't pay the 10% Early Withdrawal Penalty for doing a conversion.  Only for distributions.  Have the custodian do a direct transfer to the ROTH.  Don't get a check you have to deposit yourself.

The roth conversion would be taxable income on the return  but it is not considered earned income so you still can't make an IRA contribution ....but since your income is so low you will not pay tax on this conversion either ... a win win scenario.