This turned out to be one of those "It seemed like a good idea at the time" things, as I ironed yards and yards and yards of fabric which was tough to orient on my ironing board. To complicate matters, I had one barfing cat (something seems to be down the wrong way and she has been wheezing stuff up - will consult vet) and one, of course, energetic kitten. This made me realize soon enough that I needed to do it all at once and keep it out of Maggie's way. As it was, whenever the pile of fabric got close enough to the back bedroom door, a gray-and-white paw would emerge from under the door to bat at it. There was much loud purring emanating from the other side of the door, indicating that Maggie thought this a capital game devised for her amusement. OK, it was pretty funny.
She did catch it a couple of times, making me glad that it is silk noil and slight slubs are part of the nature of the fabric!
Now I know why M., whose perfectionism on all things Altar Guild is well known, didn't do it himself last time. I did get some validation that this was not complete folly on my part from idasusan, who called me most unexpectedly during the process (Weds. night is choir practice) to talk, and on hearing my sad tale of woe, said, "That thing needed to be ironed".
Whether the wrinkles will be back after I rolled it up on a tube is quite another story, but I think I'm beyond caring at this point.
Must look for the large-sized ironing boards like Stonemountain has for its classes. If I find them I will buy two and take one into the church for large-object tasks.