Sacrilege
Mincha according to many seforim (Halachically Shacharis is most important) is the most important or powerful Tefillah of the day because during our hectic work day we take off the time to recognize that there’s a Creator and everything we do in business or elsewhere in our lives is totally worthless without His blessing and help. We can’t succeed without Him. The Gemara says that Eliyahu Hanavi was Davening and Davening and was finally answered by Hashem at Mincha time (on Har HaCarmel)
That being said your father can be matir your neder if you never said bli neder. I don’t know all the rules but its an easy process.
If you already are Davening 2x a day make Mincha #2.Mincha is shorter than Maariv, its just ashrei shemonah esrei and aleinu I don’t even think you need to say tachnun. Look at it as though you are davening “Maariv” a few hours earlier.
You certainly have the 5-10 minutes it takes to Daven a quick Mincha. Although it may mean less time in the CR here we will all be happier knowing you are Davening to Hashem and putting Him before us.