Will you be doing the facility (UB) or professional (CMS-1500) or both?
There is a LOT of Medicare/Medicaid so IMHO I wouldn't do %. You also mention TN which is one of the states to consider some fee structures to be fee-splitting. Interestingly enough it's a state where a precedented case was made in which the PM company's contract did not stand because of that.
If you have a client coming on to which there is a lot of work to setup and they want you to work on backlog I think it's best to break up in two .. one for services day-to-day and one structure for the backlog. Strongly reccomend looking at reports to see how old claims are, status of claims, patient balances, etc. You don't want to take their word for it and price too low for a lot of work. I personally like the flat fee schedule because I base mine on hourly rate but client really doesn't see it. i then add expenses. But I never quote pricing until I have established at least a good base estimate of time needed on this account. Keep in mind, as you estimate time that they may not be your only client in the future, so you always want to make sure the account won't eat up all work hours for current staff if any.
You don't mention software/setup, will you use theirs or your own? Big deal breaker. For my business I don't maintain any software or system costs, the client does. BUT if they don't have one, once they get one or switch to another then you have to look at the time/costs and efficiency of conversions.
YOU need reports and the ability to sit down to review them before quoting them a price. JMHO