Court should of directed you both to agree on an independent QS.
Judge should of also instructed what the QS needs to report on. I.E deviation in levels as per BS****** etc.
An independent tiler is not an independent professional assessor. If thats the route the court guides you down then if anything doesnt go in your favor you can shoot down the report by questioning experience, qualifications and even integrity. Whose to say he/she hasn't got the offer of "rectifying" anything he/she may or may not pick up on.
Unless the independent knows British Standards and how to test and present findings in a report suitable for county court proceedings then its a no go in my opinion/experience.