Why go with the minimal antenna gain? ... any antenna with a 3 db point that exceeds 6.5 degrees is just wasting transmitter power.
I think that would be about a 24 dB gain antenna. Pretty big and would take some careful alignment... Kinda like a realy big EME array
Just remember what an Oscar 10 station took to have reliable communications, At Apogee it was only 35,000 miles away, the Moon is ...] [250,000 miles]
Which is 7 times farther, squared or 50 times more power (about 17 dB).
BUT one easy way to get gain is to use just a long coaxial gain cable. I think it takes about 22 feet of coaxial dipole elements at 2 meters to give about 6 dB of gain. So laying down 6 dB gain segments on the rock of the moon is as easy as unrolling a spool of cable. Unrolling 8 of these with the right spacing could yield about 17 dB.
Of course this woiuld only point straight up, so it would need to be on a moon base in the middle of the earth facing side. But since there is a lot of interest in moon bases near the poles where there might be water, then a similar array of layed down coaxial cable arrays could be phased horizontally to point at earth. Actually, just about any direction can be obtained with the right spacing.
ONLY problem of course is there has to be someone with legs to roll out the cables.
Just a thought. Bob, WB4APR