So, from what I understand, you did #1, ie, cleaned off as much stuff as possible. Next, you have downloaded and installed Onyx, and started to use its routines. When you launch Onyx, the first thing you are asked is to whether or not Onyx should verify the structure of your boot drive/partition. Did you let it do that?
The next thing to do is to Repair Permissions, which is under the Maintenance tab.
Now, from there, most of the other useful/applicable tasks in Onyx do require a restart of your machine. But apparently that could be an issue.
Also, when you say "I've done all but the Disk Utility (I've run it twice this week)", did you do that via the (hidden) Recovery HD partition? That would be the only way (with your setup) do use the First Aid feature of Disk Utility effectively.
In any event, just do that much with Onyx, ie, let it verify the structure of your disk, and Repair Permissions. Neither of those tasks require a re-boot of your Mac. When the Repair Permissions is done, you can just quit Onyx.
I'm wondering if you could try something else next. Malwarebyes is a very good anti-malware product, but unfortunately it does not pick up/isolate everything. I have Malwarebytes and do run it periodically, but it has not found any issues yet. But recently, I downloaded the excellent anti-virus software ClamXav. You can get it from here:
https://www.clamxav.com/
You can use it in demo mode for 30 days, and that is what I have done. Surprisingly (and happily!), ClamXav found some "virus-related" files on both of my Macs. I have not been having any issues with either of my Macs, but it was still somewhat "disturbing" to see some "bad" files on my machines (two of them were connected with a solid app I use, VueScan. I suspect they came from one of the downloads of updates I have done for that app, which come out frequently). In any event, I have removed them from my Macs.
After doing all that, and especially if any virus-related files were found, it could be time for a more recent Time Machine backup. But, even though Onyx can verify the structure of your disk, I am not sure how "robust" that is. I have a more robust disk maintenance/repair program, TechTool Pro, that I use for checking out my internal drives (SSDs on both of my Macs).
In any event, after doing all that above, see if the issue still occurs. If so, then you could proceed as follows.
Given that you have a backup, you can boot your machine via Command-R, use Disk Utility there to Erase and format the Mac partition, then do a clean, "virgin" installation of OS 10.12.3, and then use Migration Assistant to "migrate"/copy stuff from your Time Machine backup. You then should be able to re-start the iMac as usual. Hopefully that will work.
The (possible) one "caveat" is that whatever is causing your current issues could be on the Time Machine backup. And who knows what that can be? However, if you have nothing critical on your Mac 9except for Parallels, maybe to could just migrate the Apps from that Time Machine backup That will get you Parallels, and your other third-party apps.