How do small woofers produce large bass?

With the info gathered from the OP, we can’t give him good advice until we know the room dimensions/size. If it’s a 10x10’ room, go with small woofers, if it’s a 20x13’ go bigger. Also, the OP wants 2 different outputs from 1 set of speakers, high output with a lot of bass for HT, but then real clean bass for music. Very hard to do. I am for separating the 2 environments to 2 different rooms with different systems.

I prefer the cleaner bass of smaller woofers (a few per speaker) instead of 1 larger woofers and get a real good sub that is tuned that you can’t tell that’s even on. 
 

Not sure about your subs, but with REL subs, you can hook up both a LFE connection and a high level connection off the amp. You can configure both inputs differently so you can still get slam from HT but clean bass for music

@audiotruth 

You didn’t mention your room which will be a big factor how the bass response is but a transmission line speaker is one design that can produce deep bass with small drivers. As far as new speaker recommendations I suggest you audition Rockport Avior ii speakers. They are incredible and would be an endgame speaker. Good luck !
 

The only way a smaller driver keeps up with a larger one when producing low bass is to increase it's excursion--plain and simple

However, there is always a price to pay.  Higher excursion demands much more power from your amp AND there is a limit to excursion AND the more the excursion the more the distortion.  

The mid bass impact issue is much more complicated as other factors enter into that equation. 

In the end you will need an audition in your own system.

Generally speaking, the farther a woofer needs to move to produce the desired amount of deep bass output, the greater distortion both from the amp and the driver’s components w/ all other things being equal. This was a basic tenet of Paul Klipsch. Thus, larger woofers with higher sensitivity in bigger cabinets have an inherent advantage of producing deep bass at higher output levels but at the cost of other issues like cabinet size & quality requirements & potential effects on imaging & unwanted reflections from the midrange & tweeters. 

Like how are these 6.5" drivers going to handle something incredibly powerful/dynamic (bomb blasts/gun shots/thunder/explosions etc etc???

Not without high distortion and strain, (excursion = distortion) see here bass myths.😎

Mike