I voted "none from this set" for all. I am still in search of my favourite Linux, and that is likely to continue for a long time, given the wealth of choices available.
Wiz, while I know that it's took some a few weeks or months to find a 'go to' distro, you may be on the way of creating a record.
Most of us finds our favorite Linux OS in much less time than you, much of the reason why it took me 3-4 months was because most 'dedicated' Linux forums cold shouldered me because I was dual booting with XP at the time (early 2009) & refused to give it up until at least I was settled. Having blown away your Windows OS, you'd have been welcomed with open arms on any Linux forum for guidance, though we do appreciate you sticking with us, rather than being a floater between forums.
Being that Linux Mint MATE is your daily driver, you can't call that your favorite? Especially if you're booting into it w/out a thought, rather on instinct.
On the other hand, if you're having to decide before every boot, then you don't have a clear favorite. I can understand & appreciate why you're wanting to be careful with TimNet, at the same time, see how it could have happened. A Timeshift backup of two computers in the same folder, if the cleanup wasn't good, could result in this, though it may take years for one to duplicate the same. I once thought of trying this between Mint 17 & Ubuntu 14.04 & check out the result, just got too tied up & never gave it another thought.
Peach OSI could be a great OS, if it weren't for the poor support on the distro level, the creator has left it up to the Linux community to answer questions on various forums. Though I have to admit, would never had known it was an XFCE distro had there not been a couple of telling signs, the distro is loaded with software, likely more than any of Zorin's offerings, even their paid versions, has. It would seem that if one took the time to create a distro, to have their own active community, and not have to wait two days to become a registered member, and furthermore, censoring every post before allowing it to be posted. For these reasons, I cannot recommend Peach to anyone. I mean, what does it cost to have a community, of all volunteers, even most all the staff (admins, mods & so on), when the server is already in place?
Since Bluestar Linux is an Arch based distro, I'm not qualified to comment, other than the learning curve is steeper than any Ubuntu based one. I found the same to be true of CentOS, which is RedHat's development OS, lots of great software is included that doesn't make the final cut to include in the next RedHat version. Still, one can use the software, and the main reason why I was swayed off course with CentOS was that I, along with others, was invited to be a moderator of a Windows 8 forum, a decision that I wished I could take back a thousand times or more.
Basically speaking, if one knows CentOS, the same knows RedHat, which is used by lots of accounters, including tax preparers. Knowing this OS & how to fix things can lead to good things. Though many Linux IT Pros has a formal education, some doesn't, like you, I & many others running Linux, grads of the University of Hard Knocks. Which in the real world is good, those things are not taught, dealing with folks of different diversities (which I have lots of experience with), social status & so on. What they care the most about is you getting their computer (or server) going again & being able to communicate in terms they understand.
I would love to return to CentOS, just don't have it in me to go through the first few months all over, a lot has changed since 2012. By now, it would have been my 'go to' OS, had I not left it.
Sometimes it's hard to decide, but I believe deep down that you have a favorite of your installed OS's. You just have to make that decision.