Professional commercial artists do not charge "per look," per face or by the hour. We charge half day and full day rates, period. The only exception might be for those who do bridal and charge on a per person basis. But based on where you live, I don't imagine there are many pro artists working full time, if any. No offense intended, I live in a fairly big city and even here there is a small pool of work since it's not NY or LA.
You can probably find a newer artist who is willing to make an arrangement with you; you might want to ask how they determine their rates just in case.