R Eliezer Melamed (Peninei Halacha Zemanim 10:19) rules that one should indeed say it with a minyan despite not having eaten or changed into shoes, if waiting longer will cause a person to forget.
In our shul, we serve cake and drinks to allow people to break the fast, wash up and say the blessing together.
The custom is to postpone Birkat HaLevanah (the Blessing of the Moon)
until after the fast [of Tish’a B’Av], because the blessing must be
recited joyously, and we decrease our joy during the Nine Days. Many
people are accustomed to saying it immediately after the Ma’ariv
prayer at the conclusion of the fast, but it is improper to do so,
le’chatchilah. After all, it is difficult to be happy then, when we
have yet to drink, eat, wash our faces and hands, or put on [regular]
shoes.
Therefore, [each community] should set a time – an hour or two
after the fast – for the recitation of Birkat HaLevanah, and in the
meantime, everyone will [have a chance to] eat something and wash up.
This way, they will be able to say the blessing joyously. Where there
is concern that pushing off Birkat HaLevanah may cause some people to
forget to say it, [the congregation] may say it immediately after the
fast, but it is best to take a drink and wash one’s face beforehand.