The Gemara says בְּנִיסָן נִגְאֲלוּ בְּנִיסָן עֲתִידִין לִיגָּאֵל, in Nisan the Jewish people were redeemed from Egypt; and in Nisan in the future the Jewish people will be redeemed in the final redemption. Another Gemara says במוצאי שביעית בן דוד בא, during the year after the conclusion of the Sabbatical Year, the son of David will come.
What is the difference between redemption and Mashiach coming? In contrast to redemption, Mashiach's coming sounds more definitive.
According to the Maharsha to the second Gemara you cited, the entire eighth year is considered מוצאי שביעית. So it means Nissan of the eighth year.
But see also Rambam's general advice on this topic:
Regarding all these matters and similar, no one knows how it will be until it will be. For these matters were unclear to the Prophets. Even the Sages themselves did not have a Tradition regarding these matters and only could attempt to understand the verses. Thus, there were disagreements in these matters. Nevertheless, neither the order that these events will occur nor their details are fundamental to the religion. Thus, a person must never busy himself with the Aggadohs and not dwell on the Midrashim regarding these matters or similar issues. He must not make them dogma. For these do not result in either love (for G-d) nor fear (of sin). Similarly, one should not calculate the Ends. Our Sages have said that the spirit of those who calculate the Ends will expire. Rather, one is to (simply) wait and believe in the principle of this matter, as we have explained.