I started a bag company, https://www.missionarybag.com/, for a niche market (young adults who leave home for 18 months to 2 years). A contract sewer here in the US makes the bags and my stay-at home wife does the shipping/handling. This is our first month to hit $1,000 profit in a month in under 6 months. After spending 12 years in software development, I wanted to create something tangible. And all the ecommerce/SEO/marketing I have helped others with over the years has come in handy - learning a lot in the process. We are looking to fill some larger orders with an overseas manufacturer.
I wish I'd known about this a few months ago when I was in the market for a new bag. It meets all my picky bag criteria including not being made in China.
I ended up getting a SealLine shoulder bag which are pretty pricey but excellent.
I can't speak for the church or any particular mission, but from my experience as a Mormon missionary over a decade ago, backpacks 1) Make missionaries look like students, when they are not. 2) Are awkward on public transportation (and using them on transport is considered quite rude in some cultures). 3) Are more prone to being pickpocketed or losing things than a bag at your side/front that you can see more readily.
The other aspect is that they actually want to discourage them from carrying so much stuff. They have many problems with back pain and the such. And like the other guy said, they want Missionaries "to look professional, and backpacks are not professional".
FYI, I just tried to send you a message via the "Contact Us" link on your site, and clicking "Send" results in a classic Ruby on Rails "We're sorry, something went wrong" error page. You could be losing sales if those messages aren't going through.