Ok - currently you have 8 months worth of expenses sitting in cash, plus an additional $28k (5+ months) accessible in your Roths. Ultimately you need to decide how much of an e-fund is sufficient for you to sleep at night, but given what you have described, here's what I would do:
keep 1-3 month's worth of expenses in a savings account (e.g. $5,000-$15,000), and invest the remainder.
During a financial emergency you would first try to cashflow the expense (you have $1,300 'extra' each month, and potentially more if you cut discressionary spending that month).
Then you would draw down your e-fund from your savings account.
If for whatever reason you still fell short you would have your taxable investments to fall back on. Your final 'line of defense' would be the money in your Roth, but to get to that point you will have exhausted $40k+.