If I understand your question, it sounds like you are sort of on the right track. If your first month is "fixed", but you have to bill in 1/2, then you would have to create 2 separate Fixed Price Projects and bill each. After that it sounds like you then bill at your normal billing rate, per month, correct? If so, then just create a Time Entry every day and then at the end of the month turn those into an invoice and bill for that amount.