"I have discovered the hard way that Apple's "Migration Assistant" doesn't always preserve file timestamps"
comment: It seems that has become Apple's MO - you must discover all things the hard way.
Caveats: I'm not entirely sure this will resolve your issue or answer your question, but I hope it will help. I don't actually know what Migration Assistant does because in 12 years and 5 different Macs, I have never used it. So this answer may be a partial answer, or it may be incompatible with Migration Assistant. As a guess, I'd say use rsync after Migration Assistant - to clean up the mess it has left. In other words, rsync can likely restore not only the timestamps lost by MA, it can also restore all file metadata that may have been lost. Others here may have better ideas; my answer will be limited to rsync.
I used rsync version 3.2.4 for this answer, installed from MacPorts. I do not know if the rsync version included with your version of macOS includes the required options shown here - you may wish to investigate that instead of installing a current version of rsync.
Background: I've begun using rsync as my primary backup tool for macOS recently, and had to address some of the same issues as you: mangled and missing metadata. In my case the issue was caused by crossing a file system boundary - from APFS on my local drive to btrfs via SMB on a Synology NAS. In your case - Migration Assistant - I cannot even imagine how it could not even get the timestamp metadata correct, but you're certainly not the only one who's reported such issues.
I made some notes while working to resolve my issue, and they morphed into a "recipe" on my macOS GitHub repo. I'll try to keep this answer rather brief since most of the details are covered in that document.
rsync with metadata preservation
rsync effectively copies data from a source (the "from" location) to a destination (the "to" location). If you are using a fileserver (NAS) as an intermediary between your two Macs, these commands should do what you need. I don't see any need to involve an intermediate NAS, but it may be convenient or desirable if you want a backup. You should be able to accomplish the rsync operations over an SSH connection; the following commands illustrate the syntax & options needed regardless of whether you use the intermediary NAS or not:
from "old Mac" to NAS:
Assuming the source & destination folders are:
SOURCE: /Users/MyHome/MyData/
DESTINATION: /System/Volumes/Data/mnt/MyNAS/
From a terminal on your "old Mac":
% SRC-FLDR="/Users/MyHome/MyData/"
% DST-FLDR="/System/Volumes/Data/mnt/MyNAS/"
% rsync -rlAXtgoDivv --dry-run --fake-super $SRC-FLDR $DST-FLDR > rsync.log 2>&1
Explanation: This rsync command uses the --dry-run option, and therefore will not actually move or modify any files. It will give you a detailed log (the ivv options) of what files would have been moved or modified. Once you are happy with the results, simply remove the --dry-run option, and run again for effect. Review the rsync.log file using the "Decoding Table"
from NAS to "new Mac":
SOURCE: /System/Volumes/Data/mnt/MyNAS/
DESTINATION: /Users/MyNewMacHome/MyData/
From a terminal on your "new Mac":
% SRC-FLDR="/System/Volumes/Data/mnt/MyNAS/"
% DST-FLDR="/Users/MyNewMacHome/MyData/"
% rsync -rlAXtgoDivv --dry-run --fake-super $SRC-FLDR $DST-FLDR > rsync.log 2>&1
from "old Mac" to "new Mac"
If you can make an SSH connection between your "old Mac" & "new Mac", it's not necessary to involve an intermediate NAS. The same rsync options may be used; I'll leave it to you to formulate the SOURCE and DESTINATION folders.
Verifying Results:
The GitHub recipe includes a short zsh script that will stat all of the files, folders, links, etc between the SOURCE and DESTINATION folders. It may be run following rsync operations to verify that at least the chosen stat attributes are the same.
The rsync options presented here will do more than preserve the metadata containing the date-time stamps; they will also preserve all extended attributes. The GitHub recipe also includes simple script to compare the output of xattr -lrsvx for all files (that have xattrs) in the SOURCE and DESTINATION directories.
The stat utility that I use here is the GNU coreutils version 9.1. The find version I use is the GNU findutils version 4.9.0. Both are readily available through MacPorts, and available for virtually every version of macOS. The xattr command is a macOS utility.
