Yes front wobble is an inherent issue with trikes. The very first suspect will be the front tire. Unfortunately with motorcycle tires they have a round profile for obvious reasons but with a trike they do not lean in corners so they tend to scrub in corners which cups them making the front end prone to oscillations. If you can find a sidecar tire that will fit the front rim then use that as they will have a flat profile like a car tire.
The rake is more so a function of steering ease. The further out the front tire on a trike, the better the grip when turning. It has to do with the three points of the triangle of road contact...
Steering neck torque and bearing condition are the other contributers/controllers for wobble. With a trike you want tighter torque on the bearings as opposed to looser torque for handling on a 2 wheeler for quick reversing of direction from one way to the other(flipability). With a trike you need them to be more solid as you aren't gonna go thru the twisties at 100mph. Just don't put so much torque on them that you cause excessive stiffness and wear on the bearings themselves.
The last issue is the proper alignment of the 2 rear wheels, but that does not contribute to oscillations as much as it contributes to tracking straight down the road. Check the age and condition of the rear wheels, you do not want to use ANY tire much older than 6 years old for safety reasons...
Brakes. Try to find some kind of disc brakes and get rid of the drums. Braking in itself is a whole science. Bore size of the master in itself is an issue. Smaller bore = more pressure but longer stroke. The pad material is important as is the total contact area. Then you get into heat dispersion and eliminating gasses and material from the pads, the whole basis behind slotted and cross drilled rotors. Slots get rid of the gasses and debris whereas the cross drilling adds to total cooling area of the surface. Also, do not forget the frront brake as it does the larger percentage of braking just like in a car. Same braking issues and rules apply...
Shift linkage, well with the setup you are doing, that is an issue. Keep in mind most of us trikers use the stock motorcycle transmission so there is no difference...