At first glance, the same logic applies here as to one who starts a meal on Shabbat and gets up to Birkat HaMazon only after nightfall, with the question being about reciting R’tzei at that time. The Beit Yosef[2] cites differing opinions. The Shulchan Aruch[3] rules that the beginning of the meal is the determinant, and one recites R’tzei even after Shabbat has ended.
However, in our case, the Acharonim rule differently. Many[4] cite the Ginat Veradim,[5] who says that the reason we recite those sections of Birkat HaMazon that were relevant at the beginning of the meal, even though they no longer seem to be relevant when bentching, is that they do not form independent berachot. Examples are R’tzei and Ya’aleh V’yavoh, which are additions to the existing berachot of Birkat HaMazon. However, one should not extend the practice to reciting independent berachot of sheva berachot after the week of festivities is over just because the meal began or even ended during that week.[6]
The Pitchei Teshuva,[7] after citing this Ginat Veradim, seems to be bothered by the following question: When a man and woman who both were previously married get married, there is only one day of Sheva Berachot.[8] There is a major dispute about what one day means.[9] Some say the first day refers to all the meals the couple partakes in on the halachic day of their marriage. Others say it applies to the first festive meal that the couple partakes in, even if it takes place during the night after the wedding – technically a new day. This scenario is very common in summer weddings. While there is a question whether to make sheva berachot if this couple’s wedding meal was not held until the night, the Ba’er Heitev[10] says that sheva berachot are indeed recited at night if the meal began during the day. The Pitchei Teshuva apparently expected that the same should be true for a meal that began on the seventh day of normal Sheva Berachot and ended on the night of the eighth. However, distinctions can be made to explain why there is more logic to recite the sheva berachot at this first meal that continued into the night of the next day after the wedding than at a Sheva Berachot meal that went into the eighth day.[11]
There is a difference between your question of reciting sheva berachot on the eighth night and that of reciting “shehasimcha bim’ono” in the zimun.[12] The Ginat Veradim[13] says that one does recite “shehasimcha bim’ono” in this case. First of all, this is not a separate beracha, and furthermore the gemara[14] says that when one makes a meal in honor of a wedding, even up to twelve months later, one may recite this addition. Although we do not practice this after the period of Sheva Berachot, in a case like ours, where there are serious reasons to consider this a continuation of the Sheva Berachot period, it is appropriate to do so. Some maintain that this is true only when people outside the household take part in the meal.[15]