@"the same mountainbike"
I have never heard of road force balancing vs just balancing a tire, but the ‘wobble’ I am experiencing appears to seem slight or normal to others, while being incredibly apparent and obvious to me. Since I wrote my first post, I taken my car back to the first shop. They re-balanced and checked a few things, but said the tires are great and everything seemed normal to them. The only difference I notice in driving my car afterwards, though, is that the knocking noise from the front of the car seems to have lessened slightly.
Cause of the flat was old tires and consistent cold temperatures/ice. I woke up and found the tire was flat when I went to drive.
The rest of the repair happened because I asked the shop to check out what I thought would amount to nothing more than worn brake pads.