@DY
“What would happen if the chiyuv of the non paying member was bigger (e.g. yahrtzeit vs. avel during 11 months)?”
The first time this happened the guest would be given the honor (provided the paying member was not sponsoring a kiddush/oneg on that date). The second time the Rav or Gabbai would explain to the guest that the honor belonged to dues paying members and suggest the guest join (if a local resident).
I changed the verbiage in my answer from non-paying member to differentiate between guest and congregants who for some reason are unable to pay dues.