I would say "tight" and "chug" have to coincide somewhat to get that sound. The "chug" has to shut off the transient very quickly at some point, otherwise it becomes too loose. Hence my preference for an EMG 81 in the bridge vs. an EMG 85 even though the EMG 85 sounds a little bit fuller than an 81. The 85 may "chug" more, but is it a sloppy mess?
The Full Shred chugs and is tight, but, IMO, it is very restrained in the low end compared to say, a Demon, which I think has excellent low end chug and tightness but is thin in the mids and highs.
In fact I would say if the Custom Shop built me an ideal pickup I would want it to be some combination of the Full Shred and the Demon.
Regarding the Invader, I always found it to be a very dark pickup suitable for situations where you are playing through amps with less gain so the pickup compensates for it. It sounds like the OP's rig has no shortage of gain (I have an old Randall Cyclone 2 x 15" half stack), but then again, some people like high output pickups through high gain rigs for rhythm playing all the time. I don't as I find it becomes a sloppy mess.
If you are playing slower styles the Invader can sound very thick and full, like a JB, but in general the Invader is my least favorite Duncan pickup of all time. In the neck position in a bright guitar with the tone control at 0 it can sound like a bass.
Regarding the Alt 8, I tried it many years ago when it first came out and disliked it. It was like a Distortion but with more negative qualities. Lots of fizz--treble and presence--even backed far down into the pickup cavity, but also very powerful. It reminded me a lot of a 5150 and that amp's polarizing tonal qualities. The Alt 8 also reminded me of a Dual Rec in that the sound could be terrible or great depending on how you dial it in.
Regarding "bright" vs. "dark" guitars, for the usual mass produced poplar/alder/basswood stuff, I don't hear any huge difference. They all sound kind of neutral to me. More important to me is bolt on vs. set neck vs. thru neck as well as fretboard wood and type of bridge.
But I am generally a tonewood skeptic. I agree that there can be individual outliers as far as "dark" vs. "bright" guitars, but of my 40+ guitars and basses I don't think any of them are inherently bright or dark enough to warrant a certain pickup based on wood alone.