Trying to achieve the best within-sample RLH (fit statistic) is not necessarily the goal that you should try to maximize when running HB. What you are trying to do is use all the information you can in the data in an appropriate way to estimate utilities that will be successful in predicting new choices by new people made outside the CBC questions used in utility estimation.
In the manual, it speaks of not estimating a None alternative (if you included a None option in the questionnaire):
"We generally recommend always estimating the none parameter (but perhaps ignoring it during
later simulation work). However, you can omit the "none" parameter by unchecking this box. In
that case, any tasks where None has been answered are skipped. The None parameter
(column) and None alternative are omitted from the design matrix."
So, if you decide to not estimate a None parameter when you included a None option in your CBC questionnaire, you are throwing away probably good information. You are throwing away any task in which the respondent selected None. (Presumably, the levels of attributes shown in competition to the None tended not to be good in this task; and that's probably good information to retain.)
The None utility may or may not have much variance or magnitude across respondents, which could affect the RMS and Avg Variance when include the None utility or not in the estimation. So, that's not necessarily an apples-to-apples comparison when including the None or not in the estimation.