Your current interest on the car loan is about $68 a month. The penalty is only $12. You should put as much on the car loan as you can until you get the interest payment down to $12. I threw it into a spreadsheet and found that number to be the last nine payments, when the principal is around $2200 remaining. For those final payments, you're better off paying the interest than the penalty.
If you add in the rate on the mortgage, it changes things a bit. If you switch to overpaying the mortgage when you have $5500 left on the car, the penalty becomes more than the difference in the interest rates. So you may be better off with keeping the whole gain of the lower rate rather than the penalty reduced on the car loan.
Technically we should also consider the Net Present Value of the penalties. $12 two years from now is worth less than $12 now. But it's not a lot less, so I'm just ignoring it. Including it would slightly favor paying the car loan early.
Note that my spreadsheet is a rough calculation based on a monthly payment of $273.86. They may give you better information in your receipt. Also, check with them if you can reduce your payment to reduce the penalties. If you can pay $1300 a month now and pay $15 a month for the last four years of the loan, that would be even better from your perspective. But they may not allow that nor similar alternatives.
If you can only redraw once on the mortgage, I'm not sure that I'd pick this as the time to do it. I'd prefer to save it for an emergency. And if you would have to pay fees, it's probably not worth it even if you could redraw as often as you want. If you pay $7000 of the car loan immediately, that saves you six months of payments and about $200 in interest. Reduce the interest savings by $72 for added penalties. That's only $130 in savings from using the redraw.
In the past six months, you overpaid the car loan by about $1300 and the mortgage by $7000. Just keep overpaying $5000 over the next four months and put it all on the car loan. You'll have it down to the point where the penalty starts to hurt. Then switch the overpayment to the mortgage and pay the minimum on the car loan until it finishes. That's simpler than anything involving the redraw and still gets you good savings.
I said this above but will repeat it here. The goal is to pay the car loan down to $5500 in principal. At that point, overpaying the mortgage is a better deal than overpaying the car loan and taking the early payment penalty at the end. More than $5500 and it looks like you're better off paying the car loan even with the penalty.