Identify/create realistic DMC tests runnable in CI

**Is your feature request related to a problem? Please describe.**
[followup to #4764, where it was noticed that the deterministic DMC tests don't cover all regimes of DMC.]

We lack a strong test of the DMC algorithm in CI. It might now be feasible to add e.g. some of Umrigar's classic DMC calculations or calculations of the HEG. This would allow full testing of the fixed node and fixed phase algorithm on an ongoing basis. Currently we would only catch some types of breakage in the nightlies, after a breaking change has already been merged in.

**Describe the solution you'd like**
Cover realistic DMC runs cheaply and reliably enough that we can run them in CI. The tests should be more effective than the existing deterministic tests.

Start by reviewing issue #4764 and the existing deterministic DMC tests to understand which regimes are missing. Evaluate candidate Umrigar classic calculations or HEG calculations for CI cost and reliability; done means adding realistic DMC coverage that exercises fixed-node and fixed-phase behavior more effectively than the current tests while remaining cheap and stable.

Written by the indexing model from the issue text.