.....Anyone ever done a helical wound "Slim Jim?"
yes.
Since this is a 1/2 wave
antenna with a 1/4 matching section (3/4 overall),

Why the 1/4 matching section? Seems that takes it
nearly to the full half wave length...or close
enough not to matter much...
Myself, I would probably prefer a "gamma loop"
type matching scheme, which adds no height.
To me, 16 ft tall is no more trouble than 12 ft tall
in the real world.
I've had a lightweight 32 ft self supporting radiator
up, which was no hassle at all...And the base of that
was at 36 ft on a mast. "68 ft tall total".
That was a dual band 40m GP/ 17m 5/8 GP....Full size
on both bands, relay switched.

helical winding of this form into a 3/8 overall height
(approx. 12 ft. @ 28Mhz) might be possible.
The extremely low angle of radiation (approx. 8 degrees)
would make this vertical antenna desirable... ......................

The angle of maximum radiation will vary fairly
drastically depending on height above ground.
For a "like" sized vertical, the height above
ground will have more of an effect, than any
extra electrical length. To my way of thinking,
the advantage of the extended winding should be
the largest, the closer to ground it is.
The higher above ground, approaching 1/2 wave up,
the lesser the advantage.
Note that at high heights above ground in WL,
the 1/4 wave ground plane, and the 1/2 wave
vertical have nearly the same gain for practical
purposes. "maybe .3 -.8 db difference..."
You should consider decoupling of the antenna
from the feedline also. Radiation from the line
will skew the pattern upwards off the horizon.
This will ruin even higher gain collinears.

I like my antennas full size if at all possible.
I'm a radio bully. :/ MK