After searching on the web, I realized that Commenters often use "Amaryllis" and "Hippeastrum" interchangeably, and it's inconclusive whether they meant Amaryllis or Hippeastrum because of the historic confusion.
So here is the deal: Hippeastrums can be forced to flower in fall, the same season Amaryllis Belladonna flowers. I currently have none being forced. My Amaryllis is sending its flowering shoot already and even if I buy a "forced" Hippeastrum, I would still miss the timing. Still, no time is lost if I manage to "freeze" some pollen till spring. In my country, Hippeastrums "left on their own" are grown as evergreens and they flower in spring. Imports and local bulbs are sold while dormant and some may have even been forced to flower before reaching the retail store.
Would the kitchen's freezer provide a low enough temperature to preserve the pollen? Would the cross-offspring need a summer dormancy like Amaryllis, or will it remain evergreen like the Hippeastrum?
A note of caution, though: Modern hybrids may be triploids, as I noticed they are sterile and cannot be pollinated. I don't know if all hybrids are like this. I have few bulbs I bought in 2002 which produce seeds consistently, without any artificial pollination. I have failed to pollinate the modern hybrids I have.