I seriously doubt it's actually FSDT's CLT causing the issue
It surely isn't. See this video I made a while ago, which shows how KCLT normally performs:
And, it was taken with a lesser system than yours: i7-6700 with a GTX 980
but what steps can I take to figure out what the culprit is?
Disable all those addons (Disable, not uninstall), and see if the pauses goes away. If they do, reenable them, one by one, until you find the culprit. I'd start with UTL and AS4, since they are surely the ones putting more strain on the system.
Also, try the "Cap Simconnect updates" option in the Addon Manager, with or without it, and see if you have any improvements. Note that, in order for this to work, be sure you have installed the current FSDT Live Update.
Also, if you used any kind of Affinity Mask tweak, try to remove it and leave it at default.