Imo pay him what it takes. Sounds like he's doing a thorough job. Slow and steady. Overall final figure will still be good by the sound of it.
Interesting the number of replies on here saying to never pay a day rate. How do you negotiate extras / problems found? If these are included for then you'll be paying a higher fixed-price anyway.
Similarly, I've had older, more experienced tradesmen say that they won't work to a fixed-price as too many unknowns and too much risk.
At the end of the day you have to go on gut-feeling, trust and what sits right with you.