I Pilsbury - and keep it cool until just before using it
Make your own.
Do you blind bake the crust? And put little vent holes with a fork at the bottom and side. Make use the pie crust overlaps the edge of the pie pan and crimp it down. Line with foil and put in coins to weigh the crust down..bake about 15 mins at 375. and another 5 mins without the foil/coins/weights.
Look into getting a 'pie shield' to keep the edges from overcooking.
In general when I'm blind baking a crust (which I absolutely would with quiche). I form the crust from well rested dough. If its not rested, it will often shrink during baking. If its a particularly lean dough,. I'd build it a little higher than the actual pan. If its just a regular pie crust, I simply crimp it. I would dock the crust, freeze it, line it with a large coffee filter (personal preference, foil works too), and fill it generously with beans. If you can't fill to just under the crimp, I would dump in what you have, and push it up the sides. Bake it in a relatively hot oven (375F) until it sets. That could take 15 - 20 minutes depending on your oven. I would begin to check around 12. After its set, remove the pie weights and lining, turn the oven down to 325F, and continue baking until its lightly golden.
There is no sin whatsoever in using prepared pie crusts. The daughter uses them often. I'm frankly thrilled that you're preparing your own quiche. There are some factors that affect your one-sided drop. First, the case in which they traveled to you store may well have been dropped. More than once. More than twice. Second, your oven may heat unevenly - many do. So be sure to set your quiche on a baking sheet (a good guard against messy overflows) and rotate it halfway through its baking time. As well, I'm fond of Sam's suggestion to shield the edges from over baking. If you don't want to indulge in edge shields, you can certainly fashion some from aluminum foil.
And should you one day be interested in making your own pie shells, here is a tutorial that might interest you: https://thesolitarycook.wordpress.com/2012/07/28/perfect-flaky-pastry/
Most of all, you sound brave, and I suspect you will persevere. Please let us know your results.