Although it can't be controlled by logic, it is possible to produce a docked entity at any angle you want.
Turret mount points inherit angle from blueprints... so if you mount any docked entity on a turret point, manually aim it in the direction you want, and then save a blueprint, it will open up at that angle every time.
It isn't perfect, but it does achieve (in the strictest sense) that which you want - to break up the 0, 45, 90 angles we're currently confined to.
As examples of how I've currently used this, observe the lower arms of
my shipyard. They're all spawned in entities off the one saved blueprint... each arm consists of three generations of docked entity (ie: docked main arm, then another docked to that, and finally the tip docked to that) all spawned in at identical angles which I set on the original saved blueprint.
It's a start towards what you're asking for, at least. It just can't be ALTERED by logic (although you can always climb into the core and alter it yourself manually at any time, of course).
Another example is the wings on my
Flit Class scout/raider craft available in Community Content.
Not quite 45 degrees. Sadly limited by not being able to "fold up" for carrier storage etc, but as I mentioned, it does at least break up the angles into whatever angle you want...
I haven't yet used it to it's full potential (for example a really nice alien carrier with a ton of antennas hanging out the back at all angles like the spines on a hedgehog or something) but it can be done... they just can't be made to MOVE.
Hope that helps scratch your itch for now...