I don't think the Inequalities context will help with this, as it is just an alternative syntax for obtaining Interval objects, so would not work with the kind of notation for sorted lists that is being requested.
I think it would probably require the development of a specialized context for this. It shouldn't be too hard to do, but I'm not sure when I'm going to bale to take time for it. I'm also not sure of all the parameters that are needed. For example, will the terms always be letters, or will it include numbers? Will there ever be operations for the terms (like 10 > 2+6 > 4)? What should we say about errors like 10 > 7 < 8? Should there only be one of the two inequalities? Should there be >= and <=?