Your church is so fortunate! What a wonderful piece of history.
I inherited a couple of old quilts (although much newer than yours) and had to do some cleaning. Be very careful--especially that the red embroider floss doesn't bleed! The National Quilt Musuem site has information and you can google other info. The apprasier that checked out my quilts pointed out that the brown "spots" were actually the tiny husks of the cotton boll and seeds as the batting used at that time was not like ours now. So in other words, she told me to quit trying to get them out!(I had been using a toothbrush and soap thinking they were mildew spots !) If that's the case with your quilt, you could put up some note about the making of the quilt and mention that.
Also, she really emphasized that the quilt, if it is displayed continually, needs to be encased in a glass that does not let the light (even just regular lights, much less sunlight) deteriorate the fabric and dyes. That is expensive, but doable--even then I'd take a page from museums and not put it in an area with any sunlight.
Of course you know only wash in a bathtub--I put mine in a plastic laundry basket so there would be no tugging on seams or fabric once it got wet. And used a commercial quilt soap (very gentle). then I laid it on a clean sheet IN THE SHADE outside to dry--flat on the lawn. Need to keep checking this and make sure it stays in the shade, etc. I switched out the sheet a couple of times so that it dried faster. Was very pleased with results. I don't display it regularly and even then only in a bedroom that has no use/sunlight!