If you toss out all choice sets where that attribute is chosen as best or worst, and then eliminate that attribute's column from your design matrix, the analysis should run for you.
I think you create problems for yourself that way, especially if the attribute was chosen a lot, not least of which will be explaining the collateral damage of the recoding/data deletion.
If you want to segment on only the 28 items, I'd cluster the HB scores instead. As you note, you will of course get different clusters.