Eating Before Someone Else's Mitzva

Before doing a mitzva such as Bedikas Chometz or Bris Mila you may not eat, since Chazal were concerned that due to the eating you will not end up doing the mitzva. What if you have already done the mitzva and have promised to do it for someone else, are you permitted to eat first?
Rav Betzalel Stern (Btzel HaChochma 4:60) says that you are permitted if it is not your own personal mitzva. He gives two reasons. First, since someone else may also do the mitzva and your mishap is not fatal, Chazal did not forbid eating. Moroever even in a case where it is a Bris Mila and you are the only Mohel in town, even so says Rav Stern, for those rare cases Chazal did not institute the prohibition.
Secondly, says Rav Stern, if we were to forbid someone doing a mitzva for another person from eating, he may not agree to do the mitzva and therefore this prohibition would be counterproductive. He brings an example of Chazal not placing burdens upon those doing other people's mitzva from Mezuza. Although a person should check his mezuza twice every seven years (Shmita), a mezuza in a public place need only be checked twice in fifty years (Yovel).

[Revach.net]