(I find it a bit messy to have an empty library hanging around), especially since it didn't in some earlier versions, which let you specify the Main Library folder.
That must have been before my time. I'm pretty sure since MC18 the default library has always had to be in the "C:\Users\[UserID]\AppData\Roaming\J River\Media Center xx\Library" directory. I just checked back to MC11 in 2004, and I can't see anything indicating that was changed in that time. Cloning a library to another location and clearing the local library would leave a very small empty library as the default. That shouldn't be an issue.
My library has 15000+ files and is 867 MB in size on disk.
That can't be right. I have nearly 38,000 files and the Library is only 14.5MB, with another 336MB of thumbnails. Are the numbers above what MC reports, or just the Windows Explorer size of the MC24 directory "C:\Users\[UserID]\AppData\Roaming\J River\Media Center 24"? Because that directory in total is about 1.77GB on my HTPC, with just the Plugins folder about 350MB, and the cache is 950MB.
I know you have moved the cache, but I assume that was using the setting at "Options > File Location > Conversion Cache". Unfortunately, that doesn't include the Theatre View Background cache found at "C:\Users\[UserID]\AppData\Roaming\J River\Media Center 24\Cache\Theatre View Background", which you can't move. However, if you have a Custom Theme in Theatre View you could switch to "No Theme" and delete/move/backup the Custom Theme files. You should then be able to delete the contents of the Theatre View Background directory without causing any problem. When you turn Themes on again later the images would just be downloaded again. I don't think you will get any background images at all with the Theme set to "(No Theme)", but you could also turn off the theme "Online Media Slideshow" just to be sure. That should free up a lot of space.
Both the Thumbnails files and the Theatre View Background cache need to be on a fast disk, and preferably on the local disk where MC is installed, unless you wish to see a significant degradation of performance. In the case of the Thumbnail files, the whole point is to improve speed by having all thumbnails in a highly indexed file that allows quick retrieval of small versions of Cover Art images.
Regardless, you have a much bigger problem than the space MC is using. A hard disk, any hard disk, should never have less than, at a minimum, 10% free space. You are well beyond that. At 20MB free space left you are lucky that Windows is running at all. By all means, move the MC Library, but you need to find a lot more stuff you can move off the boot drive. Time to uninstall some unused programs, run Disk Cleanup, and move all documents, images, etc. to the other drives until you can replace the SSD with a larger version. It sounds like you need bigger storage drives as well, as 50-60GB free isn't much these days.