I like a lot of the ideas here, and I have one that would not require adding additional blocks, only additional behavior to existing blocks, using existing game mechanics.
My thought: go with the docking point idea, but use standard docking blocks to do this.
To make this work, you would link (C,V) a core to a docking block, making that docking block a kind of 'core proxy', so that when attempting to dock with the standard docking beam, the dock to which you are attempting to connect will align and connect to the linked block, instead of the core.
The alignment of both ships relative to each other would be determined by the orientation of the core proxy, making it easy to dock your ship in whatever orientation you see fit. Once docked, the ships relative alignment is fixed as it is now, until they undock.
A single collision detection would have to be performed at the time of attempting to dock, just to be sure there would be no clipping. This is similar to the current docking check, though may be a bit slower due to having to calculate the hull shell, but it still only needs to happen once. Even so, it should be a lot faster than a full on collision, because you only need to calculate of a collision is present, not the result of the collision as i think that's what probably makes the majority of the lag we see in collisions while in motion. If there is a possible collision detected, docking isn't possible.
If multiple core proxies are defined, the system should automatically choose the closest unoccupied one to the target dock. If they are equidistant, either wait for one to get closer for a short time, or choose one at random (or both).
When docking in this manner, there is no need for size restrictions. To balance this, there are two factors:
first, if the target vessel did not have a core proxy dock set up, then current docking rules apply (the target dock needs enough extenders to accomodate the ship, or docking is not possible) however, the current docking rules would calculate the size of the ship using the core proxy as the center, rather than the actual core. This would make such a proxy useful, even without both ships being so configured, to allow more efficient use of fixed docking areas.
Second, vessels docked using core proxies would share mass as current docked entities do, but would not share power or defenses. This takes care of several concerns, chiefly that docking two ships together this way won't necessarily give you a tactical edge. If anything, you are at a slight disadvantage because of the sudden mass increase, but I feel that is both realistic and reasonable. Basically both ships are still independent, but are forcibly aligned together. This means if a ship is docked in this way to an invincible dock, the ship is not invincible. Want it to be invincible? Use extenders. This prevents abuse of the system.
Finally, attempting to dock to a core proxy without a core proxy on your vessel would result in the docking system using your core as the alignment and orientation point, as docking does now.
Other than this added functionality, current docking rules would otherwise be unchanged. Ships docked in the traditional way still share mass, energy, etc but would still require extenders to do so. This makes extenders tactically useful, instead of an irritating requirement for any and all docking.
Turret docking would work the same way as standard docking, with the exception that the docked turret could rotate. Again, the core proxy would be the center instead of the actual core.
This would allow existing ships to continue to operate without modification, and it would make adding the new functionality as simple as adding or replacing a single block, and linking it to the core. The addition of this mechanic would also easily allow things like internal docking of small structures like 'elevator ships' power supply cores, escape pods, varieties of cargo containers, etc. Without leaving cavernous openings inside the ship to accommodate a bunch of unused docking area. It would also allow construction of universal hangers and docking/landing pads without too much complexity, while leaving current purpose-built docks unchanged.
Sorry for the text wall, but I hope it contributed something useful to the discussion.