John, thanks for your suggestions. To answer the points--
No, I can't suppress it by steadying anything I can reach; it sounds more internal.
No, it ain't got no %$^&* dash cover--actually it's in good shape inside (mostly) and it's a Michigan car, so not sun-challenged
Fan/shroud off the hook as far as I'm concerned; the chirp is suggestive of normally-stationary parts rubbing together, not something moving that's interfering with something. HVAC blower a possibility, perhaps more as an assembly squeaking against something on body motion/stress than as a squeaky blower as such.
It needs subframe and engine mounts anyway and I think I'm gonna wait til I get that done and see what's left. Sounds like a high-pitched metal-on-metal squeak; given all the above, I'm still open to any more ideas that may come to any of you good folks out there..
Thanks again to all-