Sorry about the rejection, but as Steve indicated, it will be a learning experience. Most big companies look to contract work out from the top. It's easier to manage, even if the results sometimes (often!) suck.
I have had excellent success over the years with funeral homes. Though some have, in the last decade or so, been consolidated by large national companies, many are still locally owned family businesses. Most have a lot of carpeting, so as to be appropriately quiet.
A quick-dry cleaning method like OP will best serve their needs. Many funeral directors in an area know each other, since many work on each other's funerals.
In this way they get to know each other, and this can result in a good rate of referrals. Just keep in mind that every funeral facility has something called a "preparation room". You probably want to know where this is. Just walking in unknowingly can be unsettling.