I've coached a MOEMS team for many years now. I would say MOEMS is basically homeschool agnostic, though they really prefer to deal with regular schools.
We only meet once a month, and I usually have anywhere between 3 and 10 students on a team. I charge $10 to participate, but it doesn't really cover all my costs, as you mentioned, primarily registration and printing the exams. I don't want money to be a reason not to join us.
Back when I had more time, I would hold 2 practice meetings in September and October so folks could try it out. I'd print out an old exam from volume 2. Then in October I'd ask for folks to pay to commit. I don't often have students drop out. It's only once a month, and people know what they are getting into when they register.
You need to schedule your exam sometime after the official exam date posted on the website. It seems some "learning centers" would offer the exam and students would learn the solutions before taking the exam at their regular schools. Sometimes performance on MOEMS exams will determine placement in advanced math classes, encouraging cheating. Which is why it's better to keep your head down as a homeschooler and not make too many waves with them. I always feel like a 2nd class citizen to the regular schools, but OTOH, I've never really had a problem with them as a homeschooler.
I schedule an hour at the library for each meeting. We begin by taking the exam. Then I have the students turn in their exams and I open the doors, so parents can start to trickle in. The 2nd half hour we discuss the exam we just took. I ask students how they solved each problem, and they describe their solution as I draw on the white board. Often there is more than one solution. Sometimes I add the official MOEMS solution to the discussion. At the end of the meeting I hand out another copy of the blank exam with solutions for the students to do at home. (MOEMS HQ does not like having digital copies available.)
I take the exams home and grade them and email the parents with the students current and cumulative scores. I log in to the MOEMS website and enter the students scores.
I really love MOEMS because there aren't that many opportunities for elementary students to learn how to do competition math. (Math Kangaroo comes to mind.) Also, MOEMS is unusual in that the exams are monthly, not annual, so the students get to know each other and learn from each other as the school year goes on. It's only an hour (or a half hour...I let students leave early if they have another commitment) once a month, so easy for a lot of people to schedule.
I don't do anything supplemental beyond review the questions the students have just taken. If I had time to do a weekly MOEMS meetup, I'd just have them take an old practice test and review it. Then once a month we'd take the MOEMS officially and report the scores.
Now that my kids are aging out of MOEMS, I have them proctor the exams for the younger kids and they lead the discussion, so there's good public speaking practice as well.
ETA: In April, they mail you an award package consisting of certificates, patches, pins and trophies. Everyone gets something. Then I schedule an award ceremony, potluck, combined elementary and middle school, to pass out awards and celebrate. It's really quite nice.
Overall, I've found MOEMS to be a big part of our homeschooling experience, and I'm rather fond of the organization. Please LMK if you have further questions.
ETA: I also want to add that if the registration fees are too high, it's super easy to host your own MOEMS season using old exams you photocopy from volumes 2 and 3. While the awards that MOEMS provides are nice, they aren't all that, and you can print out your own certificates at the end of the year. You can even make up your own rules.
Edited by daijobu, 14 April 2016 - 06:07 PM.