[S]ometimes they become more prominent again, usually for a few minutes at a time. Is this a difference in perception (something is causing me to notice them more) or a difference in placement (they've moved into the center of my field of vision for some reason and are thus harder to ignore)?
Floaters do move, but not very much. Mostly they "sway and settle" when we shift our focus of vision. Noticing floaters is likely a difference in perception, for example moving your line of sight from one which is complex to one with a simple background, for (a completely made up) example, from looking at a large painting to looking at a ceiling. The lack of contrast will make the irregularities in vision caused by floaters to stand out/be noticeable for a few minutes, maybe even be bothersome and worrisome, but it soon stops. You can "find" floaters by doing that, especially if you look into a softly lit surface, like an x-ray view box without the x-rays.
How do floaters "work"?
The vitreous humor (the very structures gel-like collagen & fluid substance in the eyeball behind the iris) starts to break down/liquify in spots as we age; this is a common and benign cause of age-related floaters. You can picture how floaters work by imagining crystal-clear jello that had set in a clear glass. If you took a hot knife and quickly swiped it through the jello, some of the jello would melt; you would see an aberration in the path of light through that spot; you wouldn't see perfectly through it. Turn the glass and the aberration would be different at different angles. That's approximately how floaters work. Some are minimal, some are more marked because of the plane of liquifaction/separation of collagen fibers. They do not "move", though, through the vitreous any more than that melted jello moves through the whole.
This morning I had a particularly bad attack of this while I was looking down and reading something...
Sudden onset of floaters disturbing your visual field are most likely not the more benign aging process of vitreous breakdown, and merit a trip (or at least a call) to the opthalmologist. Those kinds of floaters (sometimes associated with flashes) tend to be caused by vitreous detachment from the retina, and can lead to retinal detachments and/or hemorrhages. While often just isolated in nature, it can be a sign of more serious and vision-threatening retinal pathology.
I'd like to avoid a recurrence.
I don't know of any way at all to predict or restrict recurrences unless there is retinal pathology being treated by an opthalmologist.
Acute-onset floaters and flashes