According to the Sephardic tradition that egg matzah can be permissible on Passover (see e.g. http://etzion.org.il/vbm/english/archive/moadim70/02-70moed.htm), is there any reason why they would not eat most regular cookie recipes which usually can easily be finished within 18 minutes and don't generally require water (assuming it could be manufactured in a special Pesach/matzah bakery with kosher-for-Pesach flour)?
There is no reason (as far as I am aware), other than the potential of some small amount of water getting mixed in, as noted in this question. If a small amount of water gets mixed in, that would make it Chametz much quicker, as outlined in that question. (There may be some other baking ingredients that also speed up Chimutz, and those should obviously be avoided too.)
However, if one could be certain that there was no water (or received a Pesak that a small amount of water mixed in would not make it Chametz much quicker) or other agent that would make it become Chametz quickly, it would be permitted.
I have heard from a well-known Rabbi who is a former Rebbi of mine (name witheld) that he buys Kosher Lepesach flour for his wife to make cakes with using pure undiluted orange juice. Also, the above linked question gives another example of this in real life, Papouchado cookies.
I would note that with pure Mei Peiros, as noted in the Rambam in the quoted question, the time limit is not 18 minutes, but theoretically infinite. I would also note that fruit juices contain sugar, as does honey, and neither is considered to be Machmitz.