I would not rely on a single statistic to tell me which respondents are overwhelmed by the task. While a low fit measure like R-squared or RLH MIGHT be evidence of a respondent who is overwhelmed by the task, it's also possible that such a respondent could focus on just a single attribute, like price, and answer the survey very consistently (thus having a high R-squared or a high RLH in a choice-based model). At our recent Turbo Choice Modeling event in Amsterdam Joseph White from Maritz Research presented results that showed this very clearly. We just don't know from a high RLH whether the respondent is consistent because he was engaged and made very definite choices or whether he was overwhelmed and simplified his choices.
I know some analysts use a combination of measures to identify respondents who might have questionable data quality - for example did the respondent speed through the survey and did she straightline her responses? I think a combination of measures is probably better than any single measure and that the fit statistic is a problematic one to use to decide which respondents are suspect.