Eli51: Let me clarify. You wrote “while those that daven nusach sefard or don’t say Tachanun cannot.” I am not sure that your statement that nussach sefard cannot say a kel molei or make hespeidim is correct when it is only a minhag not to say tachnun. For example, there is a minhag not to say tachnun during the shivas yemei hamiluim (23 Adar – 1 Nissan) yet hespeidim are delivered and kel molei’s are made during that time.
The Aruch Hashulchan uses the expression “V’Yesh shein noflim ahl peneihem ahd achar Rosh Chodesh Marcheshvan indicating that it is only a minhag.