As a general statement,
Jet drives require more HP than propeller driven craft,
for the same sized vessel.
You will also burn more fuel with a jet drive.
Go cart engine will probably be too small.
Why you want a jet drive ?
Unless you need to traverse very shallow water, under 1 foot of depth,
or you plan to beach the boat frequently,
a jet drive is not necessary.
If you have a lot of weeds in the water, it becomes an issue.
Personally, for tropical fishing, where I might be positioned near
a reef break ,casting, I like to keep the engine running,
if I need to pull back quickly because of sea conditions.
With a jet drive, there is no neutral, when the motor is on,
you are moving forward.
I am thinking an L shaped rudder stem which will be metal pipe with the rudder blade fitted on the gape of the L and height of transom bottom to hull absolute bottom (the area that would be below the cav plate if a regular outboard was fitted)
This rudder stem pipe will take input from the pump at the top end and will output via a nozzle at the bottom. And should rotate 360 hopefully with an adapted trolling motor steering mech for maneuverability and reverse functions
As that rudder blade will tuck behind the skeg area of the hull at any degree of rotation, should be very beachable and non fouling
I really want to give this the Fiji touch and run a crab claw type sail, nothing powerful, just enough for quite cruising and relaxing occasionally
I think this setup might be an elegant solution retaining rudders for sailing while having power for regular use