Although you are apparently aware of the basic bottom line on egg matzot, it is worthwhile to review the relevant sources. The gemara[2] says that dough made with fruit juices does not leaven. According to most Rishonim, this applies to eggs as well.[3] However, there are several problems with relying on this ruling to produce various types of what we call egg matzot a suitable Pesach product. (Different brands of “egg matzos” use different alternatives to water, and eggs are just one example. We will call all of them egg matzot for simplicity’s sake. The Hebrew and halachic term is matza ashira.[4])
According to many Rishonim and the Shulchan Aruch,[5] if flour is kneaded with fruit juice mixed with water, not only can the dough become chametz, but it is also expected to leaven more quickly than when flour is kneaded with water alone. Thus, not only would kashrut certifiers have to make sure that the flour was not exposed to water before the dough was made, but also that no water was mixed into the dough, even if it was subsequently baked within eighteen minutes.
There is also a dispute between Tosafot[6] (lenient) and Rashi[7] (stringent) regarding if egg matzot do not become chametz at all or if their leavening is not complete enough to generate the consequences of full-fledged chametz but a lesser prohibition pertains. Most Rishonim[8] and the Shulchan Aruch[9] agree with Tosafot, and the Sephardic practice is indeed to permit eating egg matzot on Pesach.[10] In contrast, the Rama[11] sets the tone for Ashkenazim, reporting that the minhag follows Rashi, and it is forbidden to eat egg matzot on Pesach. The Rama concludes with a compromise: when there is a pressing need to be lenient, such as for a sick or a very old person, one may eat egg matzot. It is wrong, however, for healthy Ashkenazim to eat egg matzot on Pesach (although it is permissible to possess them during Pesach and eat them afterwards[12]).
There is an additional problem regarding the use of egg matza at the Seder. Egg matza is matza ashira, which is not valid for fulfilling the mitzva of eating matza on Seder night, even though they are not chametz. Therefore, even Sephardim and the sick should not use egg matza during the parts of the Seder where there is an obligation to eat matza. (Other alternatives for those who experience difficulty eating regular matza exist but are beyond our present scope.)
It is a good question whether putting egg matzot on the tables is a violation of lifnei iver if you know that some people who should not eat them will do so. (See Yechaveh Da’at,[13] who demonstrates that even a Sephardi, who may eat egg matzot himself, may not give them to an Ashkenazi without informing him of the issue.) If you are not aware of the status of the people at each table, then you could use rely on the principle of t’liya.[14] This means that when it is quite possible that the object one is giving to someone will be used properly, it is permitted to give it to him even though there is a good chance he will use it improperly. Whereas this is a legitimate approach to take in cases of problems that are difficult to solve (e.g., someone who runs a large store and cannot keep track of who is buying what), it is not acceptable here. First, what should you, your waiter, or your mashgiach do upon learning who is who and seeing people acting improperly? Furthermore, how could you allow those who were told that the kashrut of your establishment is good to make a mistake under the assumption that anything on the table is acceptable?
A simple solution is to have a table with egg matzot placed off to the side with a large sign that identifies the egg matzot as something that Ashkenazim may eat only when the situation is pressing. You may suggest that those with questions should ask the rabbi or mashgiach.