I believe you should have an up-front established policy that is clearly spelled out in your engagement letter that any client who submits their data after March 31st (or whatever date you choose) will not be guaranteed a timely filing without an extension. Further remind them an extension is only extended time to FILE not to PAY. If they don't pay SOMETHING with their extension request the extension is not worth anything. You might also want to add a clause to the effect of "....additional fees may (or WILL) apply..."

In addition to the policy in the engagement letter you should have a posted notice in your lobby regarding payment terms in general and highlighting the  extension policy. Do not deviate from this even once, as it could expose you to litigious clients who believe the world revolves around them. (Are there really such people?)