Hopefully this isn't a dumb question, but if I block off the boxes and they're ready to lay, will they just lay elsewhere initially? How else will I know they're ready?
I consider that an excellent question. Many pullets start looking for a good place to lay about a week before that first egg. That's when you might see them scratching around in the nests during the day. That is a sign that they might be laying soon, seeing them scratching around in the nests. Unfortunately "many" does not mean all. Some pullets don't seem to have a clue that the egg is coming even when it pops out. These are the ones that may lay from the roosts at night or drop the egg about anywhere in the coop or run when they are just walking around. Most of these figure it out in a few days but it can be aggravating until they do. The egg laying process is pretty complicated and it may take them a bit to get it right. That's why you might see some of those weird pullet eggs, they are still figuring it out. And that egg laying process includes when and where.
Usually if the roosts are higher than the nests you don't have this problem but usually doesn't mean always as you are seeing. If you can post a photo showing your roosts and the inside of your coop we might see something that can help.
Yours are 15 weeks old. The youngest I've seen a pullet lay is 16 weeks though most wait a few more weeks. If they were a few weeks younger I'd suggest waiting them out but I think Aart is right, it's time to be a bit more proactive. One possible action has been discussed. Block the nests off now and see where they sleep. Let them get used to sleeping somewhere else. After they've slept in the same spot for about a week, open the nests and see what they do. That could easily be enough to break their bad habit.
If your coop is fairly dark at night, another possibility is to go out after dark and move them to the roost. If it is dark they should stay up there. Do this every night until they get the message. Usually it doesn't take much to retrain them, but yours don't seem to be acting like normal chickens. That is probably because of the recent move.
How will you know that they are ready to lay? When you see an egg. There are several different signs that they might be getting ready to lay, but those are just clues that they might be. Even if you see those signs it doesn't mean they are ready for sure. Sometimes they can surprise you out of the blue with an egg with no warning. It is frustrating but there is no sure sign. And there is no sure age. I've had some not lay for 9 months.
Sometimes it isn't that hard to retrain them where to lay even if they start to lay somewhere else. Sometimes it is. Even if your nests are open they may decide another place is a better nest. They don't necessarily do what you want them to, they do what they want to do. I want my nests open when they start looking for a nest. It improves the odds of them laying in the nests but it doesn't guarantee it.
Good luck. I think you have time to straighten them out.