Spray basting is the way to go, in my experience. For those with allergies, I think it's worth doing it outdoors and maybe getting someone else to do the actual spraying; it's that easy.
I have tried spray basting on a wall, on the floor, and on a table. By far, doing it on a table is the easiest. I have a community center where I can go, but it's also inexpensive to purchase a pair of sawhorses and a slab of plywood at the hardware store to do it outside on a driveway (or in a garage with the door open). This can be stored in a small space when not in use.
I found the wall tiring for my arms, and also found it harder to get everything lined up. It would be my last choice of the three different ways to spray baste.
Other tips: (1) lay down a large sheet to catch any overspray, then toss sheet in the laundry. (2) Smooth out backing first, then position backing. Once centered, turn down half of the batting and spray/smooth that half first. Then flip the other half of the batting back and spray/smooth that half. This is *much* easier than spraying the entire backing first and then trying to center the batting on top.