I am not convinced that you are yoitze matonos la’evyoinim with donations to moisdes.
I’m convinced that you’re not (unless that moisad distributed food or money to evyonim on Purim).
But once one has given the minimum shiur to two evyonim, who’s to say that there’s more of a priority to davka give additional funds to evyonim rather than to worthy moisdos?