Fanny Price & Catherine Morland would be so good for each other. Fanny would bring the prudence, but Catherine is pure warmth and joy and Fanny needs that so badly. They have enough mutual interests (reading, horse riding) to get them started in a friendship and I really think they'd soon love each other.
(and maybe Henry Tilney can be a good influence on Edmund?)
I’ve said this before as well, so I’m glad to have this opinion validated! I think Catherine would be able to pull Fanny out of her shell with her genuine enthusiasm. At the same time, Fanny would be a great grounding force for Catherine. I think both of them could learn a lot from each other! On top of that, they could bond over being relentlessly pursued by a short guy they don’t like.
Henry would definitely see Fanny’s merits and call out Edmund in an effectively(but playfully, this is Henry of course). They could both commiserate over their domineering fathers and reckless older brothers, and maybe Henry could convince Edmund to read Anne Radcliffe (not likely though haha).
Henry and Catherine bring with them an energy, warmth, and humor that Fanny and Edmund would seriously benefit from. Also, Fanny’s judgment would be invaluable to Catherine and Henry. I could definitely see them being lifelong friends.