I did a google search for Exeter, and found that it's considered second to Bath in terms of fashion and beauty until the middle of the 19th century. Living in Devon, it could hardly be supposed that Lucy and her sister did not make as much use of Exeter as other young ladies living near Bath might. I could find no listings for Longstaple, could it possibly be a made up city?

Also, I think that you misunderstood Jan's use of the word "Hurry". Remember that we don't know when Mrs. Jennings ran into Lucy and Anne, only that it was some time after both Edward and the Palmers were in town. That would mark the meeting at least four weeks after the Palmers left, and maybe even longer.

"From a reverie of this kind, as she sat at her drawing-table, she was roused one morning, soon after Edward's leaving them, by the arrival of company."

"The Palmers returned to Cleveland the next day, and the two families at Barton were again left to entertain each other. But this did not last long; Elinor had hardly got their last visitors out of her head -- had hardly done wondering at Charlotte's being so happy without a cause, at Mr. Palmer's acting so simply with good abilities, and at the strange unsuitableness which often existed between husband and wife, before Sir John's and Mrs. Jennings's active zeal in the cause of society procured her some other new acquaintance to see and observe. "

See? There are no specific dates here, and life in the country moves slowly. Edward stayed for a week, the Palmers a day or two. If we figure in that it took Edward a day to travel, he stayed a week, and then perhaps a week or a week-and-a-half, the Palmers came, followed by the Steeles maybe a week-and-a-half later, it's possible to think of someone as calculating as Lucy finding herself in Exeter with enough time to find Sir John, or at least the nearest acquaintance she could contrive.

As for chaperones, they came as soon as their business in Exeter was over. It's not very hard to imagine that they were visiting a relative or friend in Exeter.