Your e-mail sounds fine. If they do not respond you might follow up with a certified letter basically stating the same thing, and giving them a definite date by which they must pay in full, including late fees. If they don't pay you'll probably want to consider small claims court. When I used to do this for a living (I worked for any attorney who did small claims collections) we always included a copy of the small claims complaint filled out with their information so that they'd realize we meant business
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There is a filing fee (it's $100 where I'm at), then there is a service fee ($49 here). You might give your circuit clerk's office a call to ask them how common it is for the small claims judge to award fees and costs if it's not specifically addressed in the contract. Around here if you don't have specific language making them responsible for all costs of collection including attorneys fees, court costs and collection costs it's about 50/50 on whether a judge will award it or not.
Hopefully the e-mail and/or certified letter will motivate them to pay and you won't have to worry about it.
Good luck!