I see a many reasons to be lenient:
In regards to brachos according to the Gra and Pri Megadim (and Bircas hamazon according to the Magen Avraham (see below)) the requirement of speaking in front of a king is described by tosfos 31b and shulchan aruch 185:4 (as understood by Magen Avraham) to mean that "even when he cannot speak in a truly appropriate manner, i.e., when he speaks, it is apparent that he is tipsy, but still, he does not blunder or become befuddled." It is considered being able to speak in front of a king.(see qoute below*) Therefore, during the seder there is no problem in saying bircas hamazon (or brachos) assuming no one gets so drunk that he cannot speak without blunder or befuddle.
The Magen Avraham in siman 91 says that there is an opinion that wine in the meal and even before a meal does not get one drunk and therefore not an issue for kevanah.
In sif gimmel there the Rema writes that nowadays our wines are not as strong and therefore we are not careful even if we drank more than a reviis.
Same Rema says that if one is looking in a siddur there is even more room to be lenient.
Magen Avraham on sif gimmel brings down Yam Shel Shlomo who writes that Mincha on Yom tov it's fine to daven even if he drank a little because it is impossible any other way. (So to in our case it's impossible any other way)
Ibid. Even more so nowadays where we don't have so much kevanah
For more on this topic see alter rebbe shulchan aruch siman 185:5 and 99
*a person who is slightly tipsy from [drinking] wine is forbidden to pray until the influence of the wine abates, even though he would be able to speak before a king without becoming befuddled, as explained in sec. 99:1. nevertheless, such a person may recite grace, as long as he would be able to speak in the presence of a king. [this leniency applies] even when he cannot speak in a truly appropriate manner, i.e., when he speaks, it is apparent that he is tipsy, but still, he does not blunder or become befuddled. [this concept is derived from] the verse: “when you have eaten and are satiated, you shall bless g‑d, your l‑rd.” now, after a person [eats to] satiation, there are times when he becomes tipsy. nevertheless, [even in such a situation,] the torah obligates him to recite grace....
Only according to the Gra and the Pri Megadim do brachos lichatchila need to be recited as one able to speak in front of a king, however the Rema writes one is allowed to recite brachos even if he is שכור. So paskens the Alter Rebbe in his shulchan aruch:
one may recite all the other blessings even when intoxicated, as stated in sec. 99[:1]. even according to the authorities who maintain that concentrated intent is required with regard to the recitation of all the blessings, [blessings recited by an intoxicated person are,] nevertheless, [not disqualified]. for an intoxicated person may have concentrated intent, for he is considered as a mentally competent individual with regard to all matters. he is considered as one who acts intentionally with regard to [being subject to] all the punishments mandated by the torah, as stated in choshen mishpat 235[:22]. it is only that with regard to the recitation of the shema and the shemoneh esreh — where a higher level of concentrated intent is required — the intent of an intoxicated person is not considered as intent. instead, it is considered as an abomination, since it is [recited in a] befuddled [state], as evidenced by the fact that he cannot speak in the presence of a king without confusion. with regard to other blessings, by contrast, even a minimal intent is sufficient, even if he is befuddled.
