America's Finest,
Non-shinny shoes must be mainly an Air Force thing these days. No one around the nearby army base carries them but, as soon as my son asked, the lady at clothing sales said "try an air force base". Nearby AFB had them on display and plenty in stock.
Here is my take on the "what if we can't get them" question... (all unofficial opinions).
In the instructions sent to you, low quarters come up in two places.
1) They sent you an authorization letter to purchase low quarters at your option. If you want to get shoes before reporting and break them (or, more importantly, your feet) in before R-Day, that letter gives you the option to do so at the AAFES price. If you can't find the shoes or if you think your feet will do fine and would just rather wait to have shoes properly fitted at WP, I think you can skip buying the shoes and no one is going to hang you over it.
2) On page 8 of "Information for New Cadets and Parents", it says:
"c. A pair of “broken-in” shoes of the following
description should be worn when reporting in: black, plaintoe, smooth all-leather, laced uppers, replaceable rubber heels, and replaceable rubber or leather sole."
The document "Instructions for Applicants Offered Admission" is even more general:
"wear one pair of comfortable, well-fitting, inexpensive,
black leather laced shoes with plain toe and
rubber heel when reporting to West Point.
You will wear these until you are issued
the regulation cadet shoe"
In my opinion, the "shoe letter" and "what shoes to report in" are really two separate issues. If you can buy the shoes before reporting and you report in them, you've satisfied both. If you can't find the official shoes, you still need to follow instructions and report in a pair of shoes that at least look like the official shoes. Why? Think about what's going to be happening on R-Day. Sometime during the day (possibly before shoes are issued), they have to teach everyone how to drill and march well enough to get through the oath parade. They don't want to be trying to teach about-face to new cadets in flip flops. Sometime during the day (possibly before shoes are issued) they are going to fit you for several pair of long pants. Shoes with the the correct heal will give a better fit than your running shoes.
There are probably plenty of other reasons why WP has decided to ask everyone to report in black, leather, lace-up, low quarter shoes but they stopped short of saying you MUST buy the official shoes before reporting and you MUST report in the official shoes.
In the end, you'll get through R-Day whether you have the right shoes or not. You'll probably get plenty of attention whether you have the right shoes or not. Your feet will hurt whether you have the right shoes or not. Two weeks from now, what shoes you owned or didn't own on R-day won't matter.
Good luck and hang in there.