Regardless of your position --- salvage the old car (puts some money in your pocket) and replace it (with a similar used one if necessary) for *less* than the cost of the repairs to the old one. Take your significant other to dinner with the money you just avoided wasting on your broken old heap.
Why would a reasonable person *ever* spend more on repairs than the money required to just replace the broken car with one that works? Irrational, sentimental reasons perhaps?
Why spend $6K on repairs if you can buy a similar working car for only $5K? Why make your net "position" $1K worse with flawed logic?
What part of this sounds "tone deaf" to you?