Wow... brace yourself for the stick you're going to get.
It says a thousand things that they weren't willing to correct and finish the job without requiring more of a payment upfront, instead of completing the job, getting the all clear from you and then getting the full balance.
I guess at the end of the day as long as you're happy with the finish for what you've paid then that's all that matters. (Could probably argue that £4k for the substandard work is probably about a going price).
I'd probably try and source some sort of profile that you could put in the corner to hide some of the badly cut tiles, and then make sure it's all well sealed so that any potential leaks are well into the future.
Yep they were shysters and it was the only way to get it finished even if it's not finished the correct way.