Have macro activate other macros based on common trigger

I have the shortcut cmd+alt+shift+1 mapped to several macros which open a different macro palette based on which application is a the front. For example, in KM, I have a palette of inserting common actions, while in a browser, a palette of common bookmarks (see image below). I have a key on an external keyboard that I want to have the same function as cmd+alt+shift+1. In theory, the macro based on this key would just type the keystroke cmd+alt+shift+1, but that doesn't work (see this post).

Is there a way to do this without adding the new key as a trigger to every single existing palette? Or should I rethink this entirely by have a central macro with a switch/case that executes specific palettes based on the front-most app? Thanks for any feedback.

The macro can either use Trigger Macros by Hot Key action to explicitly trigger the macro with a hot key.