Quote -  I've messed around with multiple distant lights and some spot lights, and intensity, and color...Still looks like something is missing.

Looks like, on contrary, that there are too many things: HDRI works well as a single light system. Sorry, I've no time just now to get tutorial links around here (there are lots!) , but I shall try to come back with. I was like you a month ago, and I can tell you in advance that it''s a famous trip.
Immediate tuto:

1. remove all lights and get back to default D|S zero light. 
2. To use HDRI, you need a Light shader plugin: Go to DAZ and buy some: My prefered is PENDRAGON, or OMNIFREAKER also. Just go to Daz, type HDRI in the search field, click GO, and have a look at the result. Read attentively all items. For first timers, that allways more instructive than trying to follow a tutorial whatever it is. Also on the Daz topic read the up-to-date hot Pendragon forum. 
3. Install your plugin (Pendragon has an excellent user manual)  and enjoy, there you are.
   After a little skill with using your baby, you'll feel the need to get some HDRI additional pictures for various effects. You'll find already mid-day HDR libraries, night HDR libraries, sunset, hot, pale, and so on, but that's for later. 

Some additional points:
-prepare yourself to spend rendering duration times multipied by ten (at least).
-IBL-HDRI lighting works fine with externals, less easily with interiors, and could be really decieving for portraits if managed by clumsy beginners. 
-never try to produce your own HDRI-s, tools for doing that exist, but are not still friendly enough. But they are coming soon, just wait for some weeks for that.
Friendly, locusSolus.