Let me reframe the situation and turn it around on you.
Let's say the car was paid off. Your only debt is your mortgage. You also have $4,300 in cash in your bank account.
Now say I come along and offer to lend you $6,700 at whatever interest rate your car loan was at (but not secured against the car - this is just a regular signature loan). That would bring your cash reserves up to $11,000. Would you take that deal?
Personally, I would not take that deal. And objectively, the deal I outlined above is a better deal than the one you're actually already in, because in my scenario, if you lose your job and times get tough, you can default on my loan with relatively little consequences (beyond the hit to your credit score), whereas in your current situation, if you default, they'll repossess the car.
Whether you pay your car off or not, your net worth is the same in both situations. The car loan is not contingent on your employment. They expect to be paid regardless of whether or not you're working, so your employment situation is moot when considering whether or not to pay off the car.
If it were me, I'd pay off the car today and put the (former) monthly payment toward building your emergency fund back up.
For what it's worth, if I were facing uncertainty, I would take the deal you are offering. Liquidity and a strong cash position is always a good thing when facing uncertainty. You might call it a war chest. I understand your position, and it does come down to personal preference, but I don't think your reframing changes the decision. Cash is good when the road ahead is uncertain.