This was my solution:
Recoil starter is from a GX390. Part number 28400-Z1C-802ZA
Putting this together was harder than it would be in the USA or Europe as the Honda 3011 was not officially imported into this country. There are no Honda 3011 or GXV340 specific parts available here. This was put together using genuine Honda parts from other models. This photo was taken part way through making it all work.
As this mower is hydrostatic there is no way to start it in stock form if the electric starter does not operate.
Recoil starter works fine and electric start works 90% of the time. To start the engine with the recoil starter the seat switch must be disabled. The black engine cooling duct under the seat requires trimming to fit over the pull starter.
Next step is fix the electric start so it works reliably. I am pretty sure it is the contactor/solenoid that is bad but I need to start digging through parts books to see whether the contactor was used on other Honda models sold here.
I was a little concerned about whether adding the recoil starter might adversely affect engine cooling but, having looked at the setup on the cheaper Honda Harmony 1011 models with recall starter, this setup is very similar so I think it will be fine.
Other parts used were:
28451-ZE3-W01 x 1 from a GX390. This is the 'cup' into which the recoil starter engages. If you can get a GXV340 specific part use that instead. The GX390 part required minor modding.
90001-Z0T-800 x 3. The three screws for the recoil starter
Weld nuts x 3. These were welded to the underside of the silver engine cover.
