Email is an interesting medium as it is one where if the recipient is in an emotional state then it is completely ineffective. No matter what you write you end up reinforcing the recipients emotional state. There does not seem to be anyway to get a person to calm down and assess the situation rationally via email. I feel the best way to handle a jerk by email is get on the phone and call them if you can.

I find trying to be "overly nice" in email can often come off as a little condescending.

If someone's being rude to me I don't mind being a little condescending.

The problem with acting happy in email is it adds more for the client to read. Most people don't enjoy reading longer emails.

Just change/add some little quirks to make it seem like you're happy. Example, instead of Regards, - Say Thanks!

With email, rather than happiness, amping up the professionalism and courtesy might be an analogue.