Why must a Hebrew slave who has to work six years only be released after the seventh year?

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In Jeremiah 34:14, we read that a Hebrew slave which has served six years must be let go at the end of the seventh year:

Jer 34:14:
מִקֵּץ שֶׁבַע שָׁנִים תְּֽשַׁלְּחוּ אִישׁ אֶת־אָחִיו הָעִבְרִי אֲשֶֽׁר־יִמָּכֵר לְךָ וַעֲבָֽדְךָ שֵׁשׁ שָׁנִים וְשִׁלַּחְתֹּו חָפְשִׁי מֵֽעִמָּךְ
_{‘At the end of seven years each of you must set free the fellow Hebrew who has been sold to you and has served you six years; you must set him free from your service.’ (ESV)}

It is odd that someone who has worked six years must be let go after the end (קץ) of the seventh year. This is a reference to a rule from Exodus 21:2 and Deuteronomy 15:12, both of which are clear about the time: the slave serves six years and must be let go in the seventh year.

Exod 21:2:
כִּי תִקְנֶה עֶבֶד עִבְרִי שֵׁשׁ שָׁנִים יַעֲבֹד וּבַשְּׁבִעִת יֵצֵא לַֽחָפְשִׁי חִנָּֽם
_{When you buy a Hebrew slave, he shall serve six years, and in the seventh he shall go out free, for nothing. (ESV)}

Deut 15:12:
כִּֽי־יִמָּכֵר לְךָ אָחִיךָ הָֽעִבְרִי אֹו הָֽעִבְרִיָּה וַעֲבָֽדְךָ שֵׁשׁ שָׁנִים וּבַשָּׁנָה הַשְּׁבִיעִת תְּשַׁלְּחֶנּוּ חָפְשִׁי מֵעִמָּֽךְ
_{If your brother, a Hebrew man or a Hebrew woman, is sold to you, he shall serve you six years, and in the seventh year you shall let him go free from you. (ESV)}

Gesenius 18th ed. lists Jer 34:14 under temporal meanings of קץ, i.e. "Ablauf", that is "ending". The only way I see to reconcile Jer 34:14 with that meaning is to understand the law as: "you may let the Hebrew slave work for six years for you and then let him go after at most one year — i.e., before the end of the seventh year he must have gone free." But such an understanding would be odd, why would the owner get the right to keep the slave for a whole year after his time of service?

Are there other possible readings for קץ, or is there cultural-historical data that makes the above suggested rule seem less odd?