I think a bit of intuition you might need here is that the delivery date for a project and its fee structure are not the same thing. You carefully negotiate delivery dates. You do not carefully negotiate the definition of a day. You will find, when you do this, that most reasonable delivery dates are just fine with most clients, even if they account for more weekdays than you're billing for.
I think that with all sane clients, you will also find that once the delivery date is negotiated to both sides satisfaction, nobody gives a shit about what happens in the intervening days. Good clients are happy to know that they're going to get something on a specific date. They are thrilled to have a black box that they can put money into and get value out of. Don't open up the black box and explain it. They don't need to know how the fuel injectors work, and if you explain electronic fuel injection to them, some of them will just get neurotic about whether it's functioning correctly.
I think that with all sane clients, you will also find that once the delivery date is negotiated to both sides satisfaction, nobody gives a shit about what happens in the intervening days. Good clients are happy to know that they're going to get something on a specific date. They are thrilled to have a black box that they can put money into and get value out of. Don't open up the black box and explain it. They don't need to know how the fuel injectors work, and if you explain electronic fuel injection to them, some of them will just get neurotic about whether it's functioning correctly.