It sounds like you are giving in instead of leaving her locked in the coop and run until she has laid the egg, even if that is the next day. That would be one way, leaved her locked in the coop/run until she learns to lay in there. It may take a week or more and several eggs.
The method I use to train a hen to use a certain nest is that I made some of my nests so I could lock a chicken in them if I wanted to. That's come in handy for several different things, training a hen where to lay is one of them.
When I have a hen laying somewhere I don't want her to I make an effort to catch her on that nest laying an egg. When I do I lock her in a nest I want her to use. Typically she lays the egg within a half hour, though I had one take 3 hours on time. Typically I only have to do that once and she learns, though I had to do one two days in a row to retrain her.
The hard part is catching her on the nest laying. That's practically always somewhere else in the coop so I lock the coop door. If I can pick her up from that nest fine. If not i break out the fishing net and catch her.
Sounds like yours is a good candidate for this method since you know when she goes onto her nest.
Try this first, simple is better. I expect she will lay in the area where the basket was instead of following it but it is worth a try.
