The beeping DIMMs (Three beeps, then a 5-second pause, repeating: The memory in your Mac didn't pass an integrity check.) are not the ones I bought from Crucial. They're the OEM DIMMs which came with the MBP and were working to at least some degree when I got it from Rita.
The Crucial DIMMs were working as expected when I got the new HDD, but hoping to return them for a refund, I reinstalled the OEMs, which is when the beeping began.
I gave the DIMMs a light brushing with a plastic eraser and unseated/reseated them 3 or 4 times before giving up on them.
A quick Google search tends to support my guess that it may be an OS problem. Here are a couple of related posts I found:
...the 4GB you have will be insufficient for Catalina, despite what Apple says. (This reports on a MacBook Air.)
...a lot of people will try to install Catalina using the patcher on a MacBook that only has 4 GB of RAM and a mechanical HDD. Let me tell you now, that is a near-SUICIDAL experience for a Mac, and this goes for all models. It will run slow as molasses, and you WILL regret it. (This reports on a patched system.)
Furthermore, the MBP in question (13'' Mid 2012) is an unusual machine in that it had an extended (4 year) production run which actually ended
after the 2014s had been discontinued, and that could mean that it may not be 100% up to running Catalina, its final viable OS version, again, despite what Apple says.
...all of which suggests the possible relevance of your item "4: A DIMM module performing below or at the lower end of the specification range (replace the DIMM)"
The acid test will be performed in a week or two when my daughter who's got the same MBP brings me the OEM DIMMs I uninstalled when she bought it.
