"This is a problem as clients are then concerned that they will get charged by the IRS for late payments, albeit the return was filed on time.  It is a problem, because the tax preparer has to be the front person answering questions when they would like to take a day off."

I see this in myself so I'm not declaring any flaw in your character or that you are not kind or not nice. Yours is an attitude of a fixer. You do not have to be the "front person".

Your main goal on April 15, April 16, April 17, April 18 and April 19, and maybe even April 20, is to be happy. It NOT to be nice.

(It took me until age 61 and a long talk with a minister on April 16 to understand that this part of my personality sometimes doesn't fit with a productive and happy workplace.)