I’m not sure it’s helpful, but you could have a quick look at my recent question
https://discourse.julialang.org/t/sde-driven-by-a-noisetransport-noise/110422
Most of it is not relevant for your problem, but I think you would easily be able to ignore those parts and just read the few thoughts I had about NoiseTransport.
At the end it seems like I do not want to use NoiseTransport for the model I had, but my doubts about it remain and I would be happy to clear them.