I don’t think I’ve seen a ten wide drive with an expansion joint on the width. Usually only see expansion used when you have two different pours. The control joints need to be about 8 feet apart or the concrete will create those for you for free. Look at pours by boobs and you’ll see a big crack spaced about that far apart on them.

I’d call up a local concrete supply house and see what Sikka flex costs per tube and try to figure up the coverage area you need. Maybe push a backer rod down in there to lessen what you have to put on it. You could do a test area and see what you think. Should be way less than 4-5k. I mean way way less. You could probably get a handyman to do it if you aren’t able to bend down that much if you go buy the materials. It’s really just like caulking work.

Or have an asphalt guy do the lower portion and then try for a repair of just what’s up near the house. Asphalt is usually like 25-30% of the cost of concrete. I detest it near a house or for a short driveway, but could be convinced to live with a few hundred feet away from the house.