Here, we are speaking of electronically scanned phased arrays, not the huge arrays of Yagi-Uda antennas that are interconnected by (fixed) phasing cables and feed networks.
Much work still needed....
First off, some requirements gathering. Just what's it going to take to do reasonable EME.
Dave Blaschke, W5UN, has a handy primer on 2m EME(http://web.wt.net/~w5un/primer.htm), from which I've taken a lot of numbers for crunching and link budget analysis. He tends to give gains in dB relative to a dipole, to which I have added 2dB, to approximate to dB relative to an isotrope (dBi), since that's what I work with.
Dave gives an absolute minimum gain for the antenna of 15 dBi, and to make routine QSOs, you need 22-23 dBi. Presumably, this is with W5UN on the other end, and he has a pretty darn good antenna, and a lot of Tx Power.
He also recommends linear polarization over CP, most likely because you can't afford the 3 dB hit for cross polarization.
Front End NF should be better than 2 dB. Lots of folks are running NF of <0.5 dB, because preamps for that kind of NF are readily available. W5UN is also sort of down on bipolar amps because of IM problems (i.e. receiver dynamic range problems)
Power.. W5UN talks about 150 Watts being a bare minimum, but that probably also includes a dB of loss in the coax, which for a phased array, it might not be an issue. 500 W is nice, and 1500W is, of course, the hot ticket. (A note... 100W out of a solidstate amplifier is easy these days, so an array of 16 T/R modules would put you in the big leagues, Tx power wise).
I note another reference gives G/T for a whole raft of antennas all the way from -5 to +1: G/T =( Ga+2.15)-10 log (Ta).. assuming 200K sky temp and 1000K earth temp (wow, that high?)
A question: 25 dBi directivity corresponds to a gain of 316, which is an aperture of (G=4pi/lambda^2*A) about 100 square meters... (i.e. 30 feet on a side. Using a basic rule of thumb that putting radiators closer than 1/2 wavelength apart doesn't buy you much in gain (although it does buy you better sidelobes and performance)...
Don't forget, also, that your radiators are unlikely to be isotropes (dipoles of some form are likely), so the element directivity might be around 2 dB or even 4 dB (dipole against a ground screen), which just adds to the overall antenna gain.
Moon reflectivity 7% (from N1BUG)http://www.n1bug.net/prop/eme.html
Free space path loss given from same site as 243 dB at 50 MHz to 289 dB at 10368 MHz
Minimum detectable signal is probably something like -160 dBm. kTB for 3 kHz BW (dream of SSB EME, of course) is -139 dBm. That -160 dBm corresponds to about 10Hz BW given real low noise figure on the receiver and low loss/back lobe pickup in the antenna (4dB all together)