Levelling quartz worktops

OK - I have got myself into a horrible situation having paid someone to fit new quartz worktops then realising that he has made a hash of the job and the bits of stone are all out of level. He has been back once to sort out the overhangs which were all out of kilter but as I say the levels are all wrong. He originally set the levels by adjusting the legs on the new kitchen units and now everything is out of level with everything else. He also managed to get the sink in slightly the wrong place so the recycling bin planned for under the other side of the sink unit will not fit. He doesn't accept that this is wrong and won't refund what I paid. When I first asked about the levels he said he would come back and adjust the back of the units but the more I looked the more I realised that this wouldn't do the job and that really the tops have to come off and the new units re-leveled again which is how they were in the first place after the builder installed them. He says he will take the tops off but at my risk if he damages the units or the joints.
Yes I was a fool not to inspect properly before paying him. My only feeble defence is that he came recommended and I trusted that he would do a good job. I have beaten myself up over this and how very much it has upset my wife so now I need to sort it out.

So my question - if I can carefully take the pieces off myself, what is the procedure for setting the benches up level once the units are back where they should be. It is a U shaped kitchen with one leg of the U being just over 1 m long, the base of the U with the hob being about 4 m and the other side of the U being 2.7 m with the sink cut out. As far as I can tell all the stone has a variation of up to 2 mm between front and back. Some of them have the thick side facing forward and some the thin side so there are steps between pieces.
I guess I have to start from the thickest piece but any help would be very welcome.

Thanks

 

Chichester, West Sussex.