Good news first: the beers are an attractive alternative.
If I try to print directly from the Pi it just prints garbage which indicates to me that I have the wrong driver.
Yes. Printing directly from the Pi would be the first and most fundamental step before adding it as a shared printer. The show-stopper is not the fact it is not shared; that's getting ahead of yourself. Put that aside for now, but I believe the reason it is not shared is that it's a global setting in CUPS, under Server Settings:
Select that first, and the Sharing concern should be fixed. "Allow printing from the Internet" is probably a bad idea but not important right now either.
A caveat applies to the rest of these screenshots: I do not have any USB-only printers to test, having seen the light back when Brother did in 2007. Everything since then has been required to be AirPrint-compatible, and I am certainly not one the the elite few on the planet with a USB-only L360. I only have USB to serial adapters, so ignore the "Connection" entries in the following. The point is that once you add the printer (inoperative driver notwithstanding) having it appear as "Shared" should not be a concern.
Oddly enough I have an a selection for an Epson L310 which yours doesn't.
So close. I think that's the crux of the problem. The list is alphabetized and goes directly from the L310 to the L364. L360 notably absent. More about that later.
So there you have a successful printer addition on the Pi, but not the right driver. After adding a driver that works, the Pi will print to the L360, and the rest (adding that shared printer to Printers & Scanners) will work.
Unfortunately this brings us to the bottom of my limited well of knowledge. The limit is I do not know how printer drivers get added to Ghostscript. I do know some drivers are incorporated within it, while others are somehow brought into it through user contributions. l can tell you is that Artifex owns Ghostscript and has sole control of how things get added to it.
To proceed, your marching orders are as follows. Contact Artifex and find out where to go from there. Specifically, find out how to add the Epson L360 to that list of printers, because I don't know exactly how that gets done any more. Chris Liddell is the guy who helped me in the past, but I don't know if he is still involved with that organization (I seriously doubt it). I wish I could get you started in that direction with additional contact names and suggestions but Ghostscript has become big business. What started off as a small community has become a behemoth, and in so doing sort of lost its way and original vision of bringing open source printing to the masses.
Maybe others interested can come up with some suggestions, but I believe that is the exigent task before you will be able to proceed.
