Your dependent variable is not an "ordinal variable" in the sense of that word in statistical practice.
An ordinal variable is a categorical variable having some type of pre-defined order. For example, in this question an expert had pre-ranked a set of companies; regression was used to see how various characteristics of the companies might be related to that single expert's ranking. In your study, each Likert item is an ordinal variable with a pre-defined ordering such as least desirable to most desirable.
Although each of your 500+ respondents is implicitly ranking your 26 items, that doesn't make their set of responses into an ordinal variable. There is no agreed-on pre-ranking of those 26 items. What each respondent is doing is making an independent choice of 1 from among 26 possibilities.
So what you have is a contingency table for two unordered categorical variables, item versus respondent category. The answer from @TomHood is a good place to start.
You do have a potential problem with a large number of near-empty cells in your contingency table, so a standard chi-square test wouldn't be appropriate. It might be possible to perform a Fisher exact test on the contingency table. With this many categories and cases, however, the standard implementation might run out of memory on a personal computer. A simulation method such as
simulate.p.value option in the R
fisher.test program might be needed.
Having each respondent choose independently one from among 26 items is related to the multinomial distribution. You thus could consider modeling this with a multinomial regression. That might not help much if your only predictor variable was your classification of each respondent into 1 of 6 categories, but that approach might provide the flexibility to look in more detail how your individual Likert items or scales correspond to respondent preferences and thus might help improve your respondent-classification scheme for this application.