Caps lock key to behave like non-toggle modifier

I believe this is all possible. In my answer on TeX.SE, I give the MathUnicode.keylayout file that I made. Essentially, my advice is: go ahead and play around with this file.

A couple of thoughts:

• The XML specification for .keylayout files is available from Apple.

• On line 22 you can see that I refer to the anyOption modifier. This refers to the left or right option key. But you can also write option or rightOption if you wish to distinguish between the two.

• I'm not sure whether caps can be treated as a "hold down" key, as you want it, rather than a "press on / press off" key.

Got this all from more recent Brett Terpstra posts, so full credit to him.

Using Karabiner Elements and BetterTouchTool, you can create a "Hyper" key mapped to control-option-shift-command (which probably won't be used by any apps as a default modifier). Then you can use BetterTouchTool to maps Cap Locks + "a" to type "=". Typing "a" by itself still gets the letter "a". You can also set it up that tapping Cap Locks alone functions as the escape key or even as standard Caps Lock.

Rather than reposting Brett's code here, I'll link to the post: A Hyper Key with Karabiner Elements, full instructions.

Some screenshots to help guide you along:

After adding Brett's code to karabiner.json, the Complex Modifications pane will look like so. No need to do anything else here.

In BetterTouchTool, switch to the Keyboard pane, add a shortcut, type Caps Lock + character, then choose "Insert/Type/Paste Custom Text" as the Trigger Predefined Action.

In the Insert/Type/Paste Custom Text sheet, type the character(s) you want and choose "Insert Text by Typing".