I can tell you one fairly foolproof method for moving ANY software installation you want from one disk to another and that's to use the DOS mklink command.
The following assumes that C: is the drive where your ED is currently installed and D: is the drive you want to move it to.
1) Find the folder where the software is installed and copy the whole lot to a similar location on your other disk. For Elite Dangerous this might be something like "C:\Program Files (x86)\Frontier" which you'd want to copy in its entirety to "D:\Program Files (x86)".
2) Now rename the original folder to something like "Frontier.bak" to move it aside (ultimately we want to remove it entirely to free up the space but initially just rename it so we can test that this is all going to work).
3) Run a Windows Command Prompt as administrator (basically find the shortcut for Command Prompt, either in your start menu or on your desktop, right-click it and pick "Run as administrator").
4) Use the 'CD' command to change into the directory where the software was originally installed (e.g. cd "\Program Files (x86)").
5) Now here comes the magic ... use the 'mklink' command to create a directory link from the current location to where the software has now been moved to, for example:
C:\Program Files (x86)> mklink /D "Frontier" "D:\Program Files (x86)\Frontier"
6) As far as ED is concerned, your software is still installed on the C: drive and everything should continue to work exactly as before. Give this a thorough testing. Once you're happy that it's worked you can simply remove the entirety of "Frontier.bak" to free up the space on the C: drive.
Disclaimer: I haven't actually tried this with Elite Dangerous but I have done it with numerous other bits of software. The only gotcha I'm aware of is that if anything (e.g. an uninstalll) ever decides to remove the software from the original install directory then it may well simply remove the link you've created, leaving everything else still over on the D: drive where you copied it. Not disastrous as you can simply tidy this up yourself but worth keeping in mind.
o7
Edit: ninja'd by James ... James, any idea of the virtues of mklink /J over mklink /D ?