This might be impossible, but is it possible to somehow update version 6 of Zorin OS so it's compatible with newer hardware and software? I love the way 6 looks, and I have a LOT of nostalgia for that specific version.
It's more feasible to take an LXDE-based distro and copy over the themes and icons from 6 Lite if I want to use a distro which looks like a 6.x release, but I like the AWN panel and other bits which 6 has. Versions 7 and later don't have my interest since that's when the current logo debuted (I'm more a fan of the blue "Z" orb)
The only way to include newer hardware is by installing newer firmware (this can be a nightmare since finding and installing just the firmware is difficult at best) or by installing newer kernels.
If you go either route, you will most likely run into library version issues and the lack of some libraries newer than Zorin 6. Adding them manually may work, but you may also find yourself accidentally upgrading to a newer version of Ubuntu.
This is a slippery slope that will most likely result in your acknowledgement that the OS is to old and unsupported to stay with it.
The newer the kernel version, the newer the base libraries version will have to be. It will have to be a careful, try and test situation. You may get away with jumping a few kernel versions, adding hardware functionality, but eventually this is what you'll run into.
Is the logo the sole reason, and good enough one, to limit yourself to Zorin 6?
If aesthetics is the main reason, you may want to take a look at this thread to see how far you can take customization. There are even some people who make ZorinOS look like MacOS, so I don't see a reason why you couldn't make it look like ZorinOS 6.
This required a trip down memory lane. I found my DVD of Zorin 6 Ultimate (32 bit) , and found an old desktop with DVD, and ran it live. A lot of the older apps like "Browser Manager" were interesting, and being able to select a background type (Video, Sound, Reset to Space background). A strange thing was no X in the top right hand corner to close a page. I had to click "Close" in the panel. I also tried many years ago Zorin 6.3 Lite as a download for my 11" notebook, but eventually used Linux Lite (XFCE) instead. I agree with Aravision that you are better to perhaps install LXDE on a modern Zorin system, and adapt it to your preferences.
Is the machine capable of running a 64 bit OS? If not, Zorin 15.3 is the newest you'll get, but still will be able to install the DE of your choice and customize to your liking.
I understand the aversion to upgrading, but with any system, you would still have to customize it and transfer your data. Right now it is more of a security risk not to upgrade.