Thanks everyone. I took your excellent advice, and sent a reply that stressed how pleased we were with the work, but that the quoted amount seemed a bit low given the difficulty of the work. I offered to pay an amount that was roughly 75% of the original quote, which he happily accepted.
I was probably making a mountain out of a mole hill, but I didn't want to be rude by either rejecting what was essentially a gift (if he was offering family rates) or suggesting that he didn't know how to fairly rate his work. And yes, I suspect the original tradie was overcharging us.