4 households chased. None by the host.

Every reminder is worked backwards from the reply deadline and sent only to the households that have not answered — at a civil hour where they are. A household that replies drops out of every later send automatically.

Step	Who it went to	Reach	Status
Invitation sent	All 12 households		Delivered
First reminder	Those who had not opened		Sent
Reply deadline nears	4 silent households		Sent
Final call	The last few, by hand		Sent
Deadline	Count locked at 26		Closed

Counted against the 156 messages this plan includes — six per guest, and this event used a fraction of them.