This is NOT potable water. It could end up in court but, for now let their health department handle it.
To go in court the well will have to be fixed FIRST. They can not file for damages that has not happed. Start talking court to this driller and he won't come back. IMO, what would be fair is to pay for the materials, fuel and labor.
I agree, it is not "potable water" and thereby that is the basis of going to court WITH a water test or multiple tests over weeks, from a lab, certified or not, showing turbidity above the government established MCL (maximum contaminate level). And dozens of dated bottles of this water over a month or more until the court date at least.
And these problems occurred as soon as their pump guy attempted to install the pump and had to set it higher than 'normal' because of a blockage to setting it deeper.
Now I'm not a lawyer, didn't sleep in a motel last night, nor have I played one on TV or radio, ever, but telling the driller that court is the next step IF he doesn't come out and do something if only tell them what the blockage is and what could be done, is a good step since
"We did talk to the driller when this first started a few weeks ago, but we will probably talk to him about our options.".
Now it sounds to me he didn't say much if anything two weeks ago when he was notified of the problems. And that inaction speaks volumes of what he is wanting or willing to do; or not wanting or willing to do.
So I would give him a call, and the seller that paid him, and see what he/they says and mention court if he/they doesn't do something other than refuse to show up.
Then I would send him/them a certified letter with return receipt request and in it tell him/them he/they have 15 days and if he/they didn't show up and do something to identify the problems and fix them, I'd file the court case.
Your solution to have the OP pay for lining etc. is only good if they want to have someone else fix the problems, and recall that other drillers don't want to get involved, and then go to court to recover their financial loss. And that is iffy and probably would drag out months to a year or more.