It possible to combine both models into one larger model? You’d have to fit the GP within your 2nd model. I think this would be the most straightforward – you’d call conditional like you did and the code should work as you’d expect.
Breaking it into two separate models, you’d have to do this but specialize it for GPs. Haven’t tried doing it though! I know it’s been a couple weeks since you posted, but would be curious to hear if you tried this and it works.