there have been some VW longitudinal powered bikes using the VW transmission. Shifting an H patern shifter might be interesting problem to solve. You might be able to fabricate an addapter to run power thru a shaft drive style motorcycle transmission. I have looked into how to use a VW DSG automatic-manual in a bike, very heavy and lots of electronics to make it work.
the dieselfighter bike and some others in europe have mounted engines transverse. They use belts or chain to drive the motorcycle style transmission. My concern is the side loading on the crank with such a setup. 4 cyl VW in USA have 5 main bearing caps so the crank is supported well. The torque from the VW motor will destroy an ultima. I have a built 1.6 IDI turbo diesel in the autocross car, I sheared 2nd gear in the factory transmission ( ok it has been used and abused for years) My 1.9 TDi motor with slight warming of tune had 200 Ft Lbs at the wheels at 1800 rpm. I can let out the clutch without touching the throttle and while letting it idle keep shifting up to 5th gear. Yes, these motors have torque. TDi will have LOTS of wiring and computer control issuses to work out. Older 1.6 or 1.9 IDI ( indirect injected - has the precup in the head) with mechanical pump only needs one wire to stop solinoid, and wires to glow plugs if you want em to work.
Those are the only solutions at the moment. Never know, some other way may appear next year. Can you design and build a custom transmission? My diesel project is on hold until what I want for a transmission is available. Until then I am playing with my CB250 and F650GS Dakar
Do keep in mind the VW4cyl are Heavy, like over 300 Lbs heavy. put that on a steel frame able to handle the vibration and you will have a bike in the 800 to 1000 lbs range.
Note: this info is for the USA where Lbs is weight not money, and kilograms is used when talking about a drug bust.
