Cool, thanks. I forgot or didn't know that the Minecraft launcher could change the Game Directory after the fact, and handles moving the files. This is why the Forge installer can be so simple, because the Minecraft launcher can move it after installation.
The issue isn't for me, but what's simplest for my players, who are young relatives not local to me.
For the record, on a system that's been running Minecraft 1.8 the sequence to do a 1.7.10 Forge installation into a separate directory is:
[*]Run Minecraft launcher
[*]Check for a profile called Forge. If it exists, rename it to something else
[*]Create a profile for stock 1.7.10, if one doesn't already exist, using the default Game Directory
[*]Start 1.7.10, quit immediately (this step may be redundant but causes no harm)
[*]Download & install Forge for 1.7.10
[*]Edit the new "Forge" profile, change both the profile name and the Game Directory
[*]Start the renamed profile, quit immediately so the Game Directory change takes effect
For someone with several keybinds, you can copy in your 1.8 options.txt to the new game directory, keeping in mind that if you set the 1.8 render distance > 16 it needs to be changed in options immediately after launching 1.7.10 before a world is loaded.
Again, thanks much!
[Edit: No files are copied or moved by either the Minecraft launcher or Forge. What happens is that if the specified directory doesn't exist, a new one is created. See also the post below from Lex Manos.]