PyMC presumably lets you warm start HMC sampling with (a) step size, (b) mass matrix, and (c) a draw from a previous fit, but you have to be careful the parameters mean the same thing. As soon as you add more covariates, the interpretation of existing coefficients changes. Just be careful not to use posterior means to initialize as those are often bottlenecks for sampling if you start there.
The problem with deterministic ADVI is that unless your fixed sample of draws is very large, you’re going to get a ton of bias. Now that may be OK, since mean-field ADVI is giving you a ton of bias already, especially in estimating uncertainty. Or you may be trying to do what Ryan Giordano et al. did in their paper on deterministic ADVI and try to post-correct using linear adjustments. See:
I would strongly recommend testing that you are getting appropriate answers with ADVI using something like posterior predictive checks.