How can I relocate an iTunes library from a Time Machine backup? I have used Setup Assistant from my last Time Capsule backup on my old iMac to start my new iMac. The new iMac has a 256 GB SSD and a 2 TB HDD. The old iMac had a nearly full 1 TB HDD.

This means when I used Setup Assistant I had to exclude from the list of things to copy, all of my Music and Movies folders as they wouldn't fit on the SSD.

I have now been able to pull the Music/Movies off the old Time Machine backup and put them on the HDD, and all the system/app files are on the SSD. So that's all good up to now.

BUT, all the guides I read about relocating iTunes from one HDD to another start with the library being in ~/Music and doing a 'consolidate'. In my case it isn't (and can't be due to space constraints) in ~/Music to start with. In fact, it's starting in the place I want it to be, HDD/Music

So my question is, how do I tell iTunes the library is now on the HDD, not in the default ~/Music location? 

If I do the relocate in the iTunes Preferences > Advanced panel to the new location and then consolidate, I'm worried it'll overwrite the music that is already there, with the empty library in ~/Music.
The preference in iTunes tells it where to read and write your files. It will not move the existing music library. You should set this to your HDD/Music, and you're done. Consolidate will then pick up the files you have left elsewhere (e.g. the now unblessed ~/Music) and copy them over for you.