I would do exactly as your plumber says " Dig up the line and replace that section" I have found that when there is that size of a root in the pipe it is "most likely" cracked. (not a good thing) To bad about the tree though.....
1. The lenth of time it will take to clog again is next to impossible to predict. Unless someone would like to look into the crystal ball.
2. We used to use Sanfax liquid and Crystal. But this will only slow the growth process down somewhat.
3. Backhoe for sure. That is a pretty big trench you will end up with.
4. I would put in a Cleanout in the 4 in. stack regardless. Doesn't cost much and will pay for itself the next time you have to lift the toilet.