I'm assuming you are dealing with an extremely small population size, such that n=9 is a census, so there would be no sampling error involved with your experiment. In that case, you can ignore sampling error, because you are surveying every member of the population.

I believe ACBC can do a very good job for understanding and predicting choices for individuals, one at a time (but, make sure each level of each attribute appears at least 3x and preferably 4 or 5 times, given your n=9 experiment). Per the documentation you read, we have broken up ACBC data sets into as small as groups of 9 for running HB and have found reasonably good results (for those subsets of 9 people) compared to when running it using the entire sample size. It's obviously better to estimate the models where each individual can benefit from a more stable upper-level model (from a larger population), but it still works reasonably well when the sample sizes are really amazingly small. HB is robust.

Given your tiny sample size and the assumptions above, I'd use HB estimation. Furthermore, to improve the resolution of the part-worth utilities, I would ask respondents (outside the ACBC survey) to fully rank the levels for any attribute you don't know ahead of time with certainty the order of preference (for unordered attributes such as brand, style, and color). That way, you can impose individual-level (customized) utility constraints on the final HB utilities using those outside ranking questions. The manual describes how to do this in the Lighthouse Studio section (use the search function to find it) entitled "Utility Constraints, Including Customized Constraints". You'll be paying special attention to the section entitled, "Customized Constraints".

It's very strange to think about conducting a predictive validation with just 9 people. naturally, respondents are not perfectly consistent. For example, a good respondent will only be able to answer with 75 to 85% consistency two identical CBC questions each involving 3 or 4 alternatives if they are separated by other CBC questions. So, given the natural variability involved with humans and your tiny 9-person sample size, I just don't see how you obtain a very robust read on validity.

Internal consistency (ability to replicate or predict similar conjoint questions answered by the same respondents) is a different thing from external validity, which usually involves at least making predictions for out-of-sample respondents (different group of respondents than who were used to estimate the utilities). And, the highest standard for predictive validity would be to predict people's choices to real world choices or purchases, rather than to predict to answers from a questionnaire.

If you could observe those same 9 respondents doing some purchase or choice among alternatives in the real world and compare the predictions from the ACBC exercise for those same events (involving the same attributes and levels as involved in the real world decision) and if you found that 8 or 9 out of 9 respondents were predicted correctly, then that might be impressive...and well exceed the null (random) prediction rate. But, these conditions are rare.