Storing household batteries
You are right that storing coin cell batteries in loose heaps is not a good idea.  Battery manufacturers warn against this.  I would store the batteries in trays or blister packs in which they came.  If a blister pack is too big to fit in my fridge, I can cut it into several smaller blister packs.

  (Source.  Page 2.)

P.S.  The topic of EE.SE is about electronics design.  The questions about use of household and consumer electronics are off-topic on EE.SE, I'm afraid.  A question like this might work in the EE.SE chat, where the rules are somewhat more relaxed.