Is $4,000 to redo shower tile in two bathrooms (under GC's insurance) a fair price?

Our GC did an awful job with the shower tile in two bathrooms, and we're trying to work out a resolution. He found an experienced union tiler who agreed to do the rework, but he wants us to pay him directly. He claims the tiler will be working under his liability insurance as long as we inform our building, but I'm concerned about this arrangement without a subcontractor agreement. We owe the GC $11k, and he is threatening a lawsuit because we waited until the second bathroom tile was almost finished before telling him to stop. I believe he might follow through as he claims to already be $6k in the hole. We'd like to avoid the stress of a lawsuit, especially with a baby on the way. We are first-time homebuyers and have never once thought about tile work or had it done before. It took time to realize that a full redo was the only solution. We fully intend to pay the GC the final invoice minus materials for the redo of work. The issue with settling and paying him for work completed is that he's completely lowballing his labor estimates for the tile work, and it definitely isn't enough to pay someone to redo it. He has refused to give us his license number, and I cannot find his license when looking up his LLC. I now know we should have gotten it up front, but he's refusing now.