No official limits on entries by air. However, that is exactly the kind of entry that gets more scrutiny, possibly because of the fact that there are no official limits. You will get much more scrutiny at an airport and you will quite likely be denied entry again unless your visa situation has changed to something more suited to long term stay in the country.
You weren't deported, you were denied entry. That shouldn't affect your extension at an immigration office inside the country. You get two land crossings on visa exemption per calendar year. so Jan 1st onwards you can do two more.
You guys should have an admins group where you can discuss all this kind of stuff in private. All the groups I’ve ever been an admin or a mod for have had one. The members of the main group don’t need to see this kind of stuff. Make your decisions in private, then make an announcement.
Flying from the UK it’s very likely you’ll need either a visa or confirmed onward travel within 30 days in order to check in for your flight. Thai immigration probably won’t ask you. Your airline probably will.
I would contact the Greek embassy in Thailand. Depending on what the Thai immigration actually want, I know they like an official stamp, so perhaps the Greek embassy could do that? Then it's quite likely that immigration would want to see a Thai government stamp on the translation which would be from the Thai MFA. Or, if the Greek embassy won't authenticate the certificate, maybe just the Thai MFA stamp on the translation would do. What exactly did immigration say they wanted with regard to the certificate?