I think they would be similar to other leeks - you have to wait at minimum until pods are clearly formed and plump, and ideally if there is time to mature on the plant, you wait to harvest like other alliums, when you see the pods are starting to open and the happy glint of a black seed waiting to tumble out. If they were looking that mature, maybe some seeds had already sprinkled out?
My season is often too short to mature leek seeds in the field by any means, not to mention turning wet! But if they can get to the stage of forming good pods, I can cut the stem about a foot long, and put the whole thing upsidedown in a paper bag, and hang it for a long time, couple of months before they will dry down, but you do get viable seeds eventually if the pods were mature enough, not so many if they were just starting.
One thing I noticed, it is easier to get the seeds out when the pods matured on the plant and were ready to split open. The ones that matured and dried slowly in a bag don't always split open as easily, so it's more of a job to remove the chaff.
The seeds that stayed out on the heads sure look viable!

Very cool look, the gar-leek with a green head of hair.
I've never even tasted elephant garlic.. rarely seen in the supermarket, at prices some prince would pay

. Must be good stuff..
If you do manage to save a head of seeds some year, put me on your list of eager swappers.