Here's an update on this. After weeks of little traction with X-Rite support, thanks to the guy handling my case I finally have work-arounds for two separate diagnosed problems. Well, I call them work-arounds. X-Rite calls it "methodology".

I expect my support case will be closed, and will await some future software update that may make things work a little better. But at least right now I have a way to get work done with my i1io.
Diagnosed issue #1 is one I believe is caused by i1io firmware 1.0.8. It hasn't been confirmed, and in fact even suggested that the firmware is not the issue despite a description of changes made from 1.0.7 -> 1.0.8 that point a smoking gun to this user, having a 30-year IT background as I do. I presume normally when using a target on for example US letter sheet, one aligns it on the i1io scanning table in a horizontal layout, with the sheet fully within the black lines on the electrostatic mat delineating the scanning area. If you do that with firmware 1.0.8, the hardware will fail to even attempt to scan the target sheet in dual scan mode.
The work-around suggested by X-Rite support, which I've found works, is to instead orient the target sheet vertically on the table. (I may have tried this eventually, but hadn't thought of it yet. No longer used to the mental mechanics needed to fully deal with technology diagnostics & work-arounds, I guess.) The top & bottom of the dashed line around the patch region most likely will fall outside the black lines on the electrostatic mat. However as long as the patches themselves fall reasonably within the mat's lines, the i1io will now read everything fine. Since one of the changes made in firmware 1.0.8 was to tighten up arm movement limitations to prevent some situations where it could swing out of its intended range and be damaged, I infer a bug in the logic that screws up normal layout reading in dual scan mode. But who knows. Vertically oriented sheets on a horizontal delineated scanning area is now the approved "methodology".
Diagnosed issue #2 was getting compounded into the first one, until I starting separating out variables & trying to isolate things. This one is a combined X-Rite and Adobe issue, and relates to the long known thing where the Adobe Color Printing Utility (ACPU) slightly downscales target sheets printed on the Windows platform. In my case, the patches come out about 4% narrower and shorter than they should.
The i1io will begin to read a multi-page set of ACPU printed target sheets, and often gets through several of them successfully. But eventually it fails in a scenario where the scanning arm moves over the entire page, line by line, as if everything is proceeding normally. But i1Profiler has become completely disconnected from the hardware, and stops reading measurements, or giving any kind of response to anything. The application sits there doing nothing until the arm finishes covering the page and resets back to the home position. Wait however long, but the application never moves forward and at this point the workflow is dead in the water. I never got a successful full reading of ACPU-printed, downscaled target sheets, even though many of the sheets appeared to read fine at the start of various test runs.
A work-around here is to upscale the target TIFF files prior to printing them via ACPU. Then the i1io reads the entire set just fine, as long as work-around #1 is followed. It's possible that using a larger patch size might succeed with ACPU targets, without having to upscale the TIFF's. I have yet to test that specific point with ACPU printed targets. I kind of suspect a firmware 1.0.8 problem on this one too, related to target sheet layout logic problems. Again, who knows.
Hopefully this may help somebody else avoid a month of downtime. Simple work-arounds in the end, and in my own defense I might have eventually figured them out without waiting for X-Rite support. But it certainly is annoying to have ridiculous issues like this with supposedly mature, reasonably high-end products.
And of course, these are just the issues that were totally preventing the i1io from working at all. Other more "normal" i1Profiler issues remain, like the application losing communications with the i1Pro partway through a scan run. Or the application crashing at various points for no obvious reason. These things happened before with manual target sheet scans. I've learned to live with them, now at least the i1io will make re-running the targets faster...