She must be very hormonal! I hope you find a solution for this. I can relate since I have Marshmallow but she only laid 10 eggs so I can't compare her to your Trilly (I am not saying that 10 eggs is a little, I am just comparing her to Marsh )

I don't know what happened to make her change her mind, but Trilly has stopped plopping eggs everywhere.
Frank is still a bit obsessed in finding dark spots, but nothing compared to last week!
I eliminated almost completely wet food, took away all the small cages so they now sleep all together in the huge mesh one, and built three really heavy blinds so that I am able to fool them completely about the day/night cycle.
I hope the eggless period will go on for a while, possibly until next autumn.

It sounds like the hormone control is finally starting to work!

With my birds, their hormone level seems to depend more on whether the days are getting longer or shorter rather than on the actual length of the days and nights. If I allow natural light conditions and the days are getting longer, they want to breed, and they start feeling the urge in January-February when the nights are more than 12 hours long. If the days are getting shorter they lose the urge, and I can stop using hormone control techniques in July or August when the nights are less than 12 hours long. Your birds may be different, but sometime after the summer solstice in late June you can cautiously stop using hormone control and see what happens.

So I should basically make nights longer (14 hours I'd guess) until July or August when I can shorten them to, say, 10 or 11, and see what happens.
OK it makes perfect sense.
Would the long nights "illusion" work even if I put up the heavy blinds but let them out of the cage for a while? Or I will need to put them to sleep as soon as the room is dark?
Sometimes they like to come perch and nap around me at night if I'm there with the laptop, it's so sweet I let them do for a couple of hours. But I don't want to ruin the night effect!

You need to keep it dark in the room for the whole "night". Their hormones are regulated by the amount of light that's hitting their eyes, not by whether they think it's dark outside. If it's dark outside but you have the lights turned on inside, their bodies think it's daytime.