Ok, for anyone that finds this thread while trying to accomplish the same thing as me, I believe I've figured this out on my own. I'm not sure if every step is necessary and I've only done a little testing so far, but the response time is down to a few seconds instead of 30 seconds or more.
On my phone :
I installed Xposed (I had already rooted my phone),
I installed the App Settings module and enabled it,
I set Tasker and all plugins to "Resident" in the App Settings module (overriding their settings),
I went to Settings -> Battery -> Options -> Battery Optimization -> "All Apps" dropdown and set Tasker and all plugins to "Not optimized".
I now have almost immediate execution of my commands with both "NFC Starter" and AutoVoice.