I think get_latest_checkpoint_with_hyperparam is just so that to not waste the existing effort accumulated on a particular hyperparam combination.
If you are not concerned about that, and just want to resume searcher state, can you try something like the following in the 2nd run?
hyperopt_searcher = HyperOptSearch(...)
hyperopt_searcher.restore(...)
tuner = Tuner(function, param_space, tune_config=TuneConfig(search_alg=hyperopt_searcher))
tuner.fit()
?