This is a great question and I'm glad for the research you've already done on the topic!
The reason we didn't include Latent Class MNL as a capability within the ACBC software is that the prevalence of respondents sorting concepts into the "possibility" vs. "not a possibility" bucket from the Screener section is captured in the "None" parameter, and this could very significantly drive the Latent Class MNL segmentation. You might find segments that were strongly influenced by "yeah-saying" bias, or the propensity to be agreeable in the screening section. We didn't want this.
However, I strongly recommend using the normalized (to Zero-Centered Diffs) ACBC utilities (not including the None parameter) in latent class clustering or K-means, or Sawtooth Software's CCEA system for cluster ensemble analysis.
In other words, you run HB and take the zero-centered diffs normalized utilities. Delete the column for the "None" utility; but submit all the other part-worth utilities to the k-means clustering, CCEA ensemble clustering, or latent class clustering algorithm. By the way, Sawtooth Software does not offer latent class clustering software (but Latent Gold software does).
Again, to clarify: Sawtooth Software offers Latent Class MNL for CBC and MaxDiff. Latent Class MNL is not available for ACBC within our software. Latent Class MNL is a procedure for estimating part-worth utilities while simultaneously detecting segments. Latent Class clustering is used when you just have basis variables but no dependent variable (e.g., normalized part-worth utilities are the basis variables).
Hope this helps!