As it turns out, quite a lot can go wrong, but sometimes newbie luck is almost as good as skill.
It was easy to weave with Homespun – my selvedges were good! But, somehow the warp wound around the warp beam a lot more tightly at each selvedge than in the middle. So of course the resulting fabric was shorter at the selvedges, longer in the middle – an unintended, undesired ruche effect. I also wove much more tightly at the beginning than at the end, with unfortunate (or comic) results for the drape of the shawl. Both effects, obvious to the hand, were subtle to the eye and difficult to document with my poor digicam, so there's no pix of the sorry fabric. Perhaps that's for the best.
Fortunately, because I still don't have a good sense of how much warp translates into a given length of fabric, I wove 'way more cloth than needed for a prayer shawl. That gave me leeway to cut off most of the tight end and to gently spread out the remaining weft across the remaining warp. The process probably would have been impossible in wool yarn, but is do-able in slippery acrylic yarn like Homespun. After several days of patient spreading whenever I watched TV (a process that may include posteriors as well as wefts), I ended up with a shawl that still was denser at one end and airier at the other, but not quite so inordinately so. I made some twisted fringe and called it a Finished Object. I am really loving twisted fringe.
DH thinks the FO is kinda bright, but I like it. Ordinarily, I like a wider prayer shawl, and I do find myself wishing for wider weaving width... a dangerous wish that I'm keeping firmly suppressed. If I stick with rigid heddle weaving, I could see wanting a simpler, smaller loom for quick samples and experiments, and a bigger, more capable loom for bigger projects. The rabbit hole beckons....