First, it's worth using the magic search button to get a feel for the woes of others - like me! More importantly, the search will give you a wealth of top tips on putting the thing up/down, storing, folding, including things like cut water bottles, plastic sleeves, towels, etc.
I have a newish top. I leave it up unless I want to drive with it down, but always (almost) put it up if leaving the car. It means that in the Summer it goes up and down more than needed, but I think it seems to keep its condition better by being up.
My top, and the one it replaced, are a nightmare to get up and down. I can do it on my own, but it's far easier with two. I've seen several cars on which the tops open and close with one hand - but more that have challenging tops. If you want to avoid the corners turning up, follow the tips a search will produce (mostly about folding corners under when stowing and using plastic sheets to ease the top into the box).
If you want to have a play with your top, there are a number of areas for adjustment, including the rear locking mechanism (inside the box); the soft top lid, and of course the soft top frame, which has numerous adjustments. There's also techniques for stretching the top on the site - not sure how effective they are.
Anyway, I'd suggest you're not alone. If you haven't already tried, you may want to see what adjustments make a difference. I'd just offer that moving the frame would be a bad idea if the top fits will when up - which is more important that the top fitting well in the box. Finally, not that there are different ways to latch the top (the manual differs between models - no clear agreement on why or to what effect). You can part latch the front, then secure the back, then fully latch the front, or versions thereof. Note also that you should ensure the two front levels are fully retrated before closing the soft top box lid, and that the two rubber stops are in place inside the lid to protect it.
JH