Yes, there is a way to run a script with K-E. Look on the Complex_Modifications section of preferences. Then look at the "Add Rule" button on the bottom. Press that and then select "Import More Rules from the Internet" at the top of that screen. That will launch a web page in your browser that points to customizations.
Scroll down to "OS Functionality" and Import "Launch Apps". Once that's done, look in ~/.config/karabiner/karabiner.json. The rule will be there and you can see how the programs are launched.
Takayama has been on a roll and after refactoring Karabiner into Karabiner-Elements, he's seems to have cracked the code to allow mapping multiple keys to one key in the last several months. That was the critical bit of functionality that was missing from Karabiner-legacy. Of course, there's a lot of legacy functionality that is still to be added but a lot of it is there now.
I was able to remove my somewhat flakey Hammerspoon implementation and go back to Karabiner.
Right now, I'm using my TAB key as a super-Hyper key to launch or focus applications. Unfortunately, pressing CMD-TAB is sometimes flakey. I'm trying to debug that.
Also, the .json format is not the easiest to work in even if you have a nice powerful JSON editor such as Atom. I'm sort off thinking about writing a YAML processor that will make it easier to assemble working key configurations from bits and bobs of JSON files. I don't have time for that now, but I'd really appreciate such a utility.
Welcome back!