Split up the path in more handle-able sub-segments. Even when split, you can simply set the Trim Paths to operate sequentially and retain the illusion without much hassle. That and of course it may make all sorts of sense to work with multiple layers/ shape layer groups and those smaller segments in the first place.
this is a very helpful tip! for... next time
(only because i had completed about 90% of the shape and wanted to just bang out that last 10% without coming up with a new strategy)
anyway, i think i figured this out. i'm more convinced now that this was a precision problem after all. not only was the shape very large, but it turns out --perhaps because the original path came from photoshop and was copied into this session-- the anchor points were all situated extremely far from the origin of the shape layer itself. so for me to even move the shape into the view of the composition, it had X translate values between 10,000 and 30,000 pixels. the numbers required to display not only the transform but the anchor point offsets FROM that transform, i believe, are what pushed me over the edge, and beyond the limits of precision.
my solution was to select all the anchor points and drag them closer to the shape's origin (this explains observation #4, since the origin happened to be screen left). this allowed me to use less extreme corresponding translation values. between this and shrinking the size of the composition i was using for this scratch work, i can describe the same shape using numbers an order of magnitude smaller. i'm now well within the precision bounds, and can move the points freely once again.
so it's not that my shape was too large, exactly. it's that it was too far from the origin, so the numbers required to describe it were too large. this doesn't mean the shape *can't* get too large, of course, which is why Mylenium's suggestion is a very good one that i'll try out next time.