[Cue insane laughter here!]
Well, it turns out the old dryer was just small enough to fit through the door to the laundry room, which is a sliding pocket door off the kitchen. No problem there. But of course, the new dryer was about an inch or so too wide an each side! M (the parishioner) and I looked at each other. M suggested we break out the trim on one side of the door in order to get the dryer through. I was dubious, and suggested, since M is a certified electrician, that perhaps we could take the top and front off the dryer and fit it in that way. he agreed to try, and we scraped up the tools needed from down the basement. We disassembled the dryer and in the process gave it a thorough cleaning. M is nothing if not very complete in whatever he does. So we then tried to get it through the door. Of course it wouldn't fit - there were some protruding pieces on either side. So we got both pieces off, and it still wouldn't fit! So we concluded that yes, the trim had to go too. So M took a big screwdriver and pried the trim off on one side - four pieces of wood with probably thirty nails. We then barely got the dryer to fit through the door - basically it was just the metal shell, with the drum, top, and front completely taken apart. Even then it was very tight, and we had to shimmy the dryer through the opening a bit. But it finally got in.
We proceeded to put the dryer together and actually had to do so twice, as the first time we forgot to put back some important pieces of equipment. So we got it hooked up and plugged in, and voila! It started right up. Much quieter than the old one, definitely!
There was only one teensy-eensy problem: no heat. The dryer was merrily spinning away and putting out no hot air. Arrgghhhh! By this time it was 9:30 at night - three hours after the beginning of a fifteen minute job. At that point M had enough and plus had to get an early start to work the next morning. So I have a disassembled dryer in the laundry room!
More as it happens, and many many thanks to M for taking the time to work on this!