As discussed on this question, there are Talmudic opinions (e.g. in Rosh Hashana 31a and Sanhedrin 97a) that Moshiach must be here by the year 6000 AM (whether stated explicitly about Moshiach or whether indirectly by saying the world as we know it will last only 6000 years), which is a widely-accepted belief. However, answers on this question indicate that it is not fundamentally required to believe that the deadline is correct.
With that in mind, are there any opinions of a specific deadline for Moshiach set after the year 6000? For example, is there any opinion in the Talmud or rabbinic writings that Moshiach has to be here by the year 7000, or 60000? I do not mean whether there are opinions about taking years non-literally, but rather whether there are explicit opinions indicating a specific deadline later than 6000.