I think the actual date of the service has more to do with availability of the KH than it does with tradition.
Maybe they made accomodations for family to be able to attend??
Regarding the 'inactivity' of the deceased, my experience goes way back to the 70's on this one. We had several deaths within a short period of time. 2 men were non-witnesses of respected women in the cong. Both had a history of being opposed to the 'truth' but one of the men ended up having a KH memorial service.
In this case, apparently it was at the discretion of the elder body. The man had recently had a softening of his heart and was a regular BackCall (Return Visit, if not Bible Study) of one of the elders.
So, I don't think there is a traditional, set time. It's all about convenience, availability and who you know...
-Aude.