I think I found an approximation–workaround to this problem via domain knowledge: remembering how I modeled Bernoulli trials x_i \sim Bernoulli(e^{-t_i / (B^{i-1} H) }) for my first set of experiments, I realized I can replace h_i \sim B^{i-1} H with an approximation e^{-t_i / h_i} \approx k_i / 100 and pretend that k_i \sim Binomial(100, e^{-t_i / (B^{i-1} H)}).
It’s really a grotesque hack but I don’t think it’ll ruin my analysis.
However, I am curious how to handle this properly via Jacobians!