My last car loan payment was 6 years and 10 months ago.

I stopped paying my car loan almost 7 years ago. The engine blew and I paid to have a shitty mechanic replace the motor and they did a bad job. I paid $3,000 for the job and it still didn’t work. I was 20 years old and couldn’t afford to continue paying the car loan payment and save for a new car, so I just left it at the mechanic shop and never went back. I’ve read that defaulted car loans fall off a credit score after seven years. My credit score is currently 573 and I’m hoping to get a mortgage and car loan within the year. I have a really good job. Right now I’m making a little over 5k net pay per month. Is it worth paying off the old car loan or just waiting 2 months for it to fall off the credit report? Also, should I wait to get a new car loan until after I get a mortgage on a house? Any advice on what to do will be very appreciated.