Thanks @maxbiostat and @bbbales2, using Stan 2.26 seems to solve the integrate_1d errors to a sufficient degree.
Unfortunately, for reasons specific to my use case, I need to use rstan::log_prob on the resulting Stan model. Which means I have to use rstan and hence Stan 2.21.3 :(. I guess I can have a crack at installing this experimental branch of rstan by @hsbadr that seems to incorporate 2.26.