A 100W and a 8 el yagi has made many EME contacts as reported in the ham rags. Its all about timing and pick the best times to do it (join an EME group) Dont point at a noisy part of the sky. There are several huge stations around the world that are constantly monitoring and glad to work a new call.
Use little to no elevation wait until the moon is heading to the horizon and take advantage of the ground reflection gain.
Ive heard my echos many times at the horizon on 50, 144, 222, and 432 running 1200, 1500, 1500, 400W respectively and 8 el, pair of CC 4218XL's, modified single long boom CC 220 (A resized 3219) on 222, and stacked HB 24' booms on 432 also respectively. Except for 6 they were well out of the noise and 6 was Q5 copy. All bands had very low home brew NF preamps confirmed at a yearly VHF/UHF conference.
Ive never made an EME contact and just ping the moon a few times a year to confirm station performance. Ive had several QRZs in return but never took the time or interest to learn the protocol as EME simply didnt interest me....neither does FT8 on MF/HF or whatever is used on EME these days.
Carl