Whenever you have a job like this, that "sounds" easy but it labor intensive, it's best to have a couple of contractors out, hear what they have to say, and their quote. By the hour is never a way to pay for a labor intensive job. But then you can run into the issue of a shoddy job if they underbid to gain your business. No self respecting person should have to underbid to get some work. Like the guy above said, he loves to be the one to come out and do it right for what the job should have cost. Sucks to be the home owner, since you're paying twice.
We live in the house that's been remodeled with the easily found craigslist contractor. Guess what the spring time project is, ripping off the front porch and starting over because some college dudes showed up and did it all wrong. Not supported correctly, not level, boards aren't even cut straight. Can't even reuse the materials. We replaced the plumbing regulator. What fixed it before? A sock in a bracket to keep the knocking pipe from being loud. A "professional" plumber said it didn't need done. On going plaster repair, can't miss it where it needs done. LOL You can tell exactly where some mud was thrown in and painted over. Don't even get me started on the electrical. Let's just say, there's some outlets we choose not to use after seeing where they tie in and how.
Always get a 2nd opinion. Always shop around, and not by price. And try to use word of mouth from people you know, and shop on Angieslist instead of craigslist, for example.
With the job almost done like it is, you can make a new arrangement with him in terms of payment, let him go and finish it yourself, or get some other professional opinions and start all over. For what you have in it already, it's not that bad. If he stops cutting up the stones they'll be reusable at least. Being a tile guy, he should have known to continue working out from where he started. But maybe he's not that good of a tile guy either.
If you want a nice design where walkways meet, you do that first and work your way out. You never bring it in to meet, because you end up having to make it fit and it doesn't look as pretty as it could have. You wouldn't start a tile floor in 2 different areas to meet in the middle... you do all your cutting in the corners/edges so it doesn't show flaws dead center of the floor.
Is it so far done that there's no point in stopping him, or is it early enough to have him redo a part of it? (negotiating a per-job price, don't pay hourly to redo something!)