if you happen to be able to read german language, have a look into Frank Schätzings book "Limit"... I don't know if there is an english translation. Anyway, its about a company that's basically the only installation on earth that is able to yield He-3 from moons surface, but they didn't loose all ties, because they made their head start by building a space elevator (which happens to be located at a us-owned island if I recall right). And... well, its a long time since I red that book.
Anyway, please keep in mind that your moon-base will have a hard time being self sustaining. And at all you might need to do to put pressure at them is taking care of their earth-side operations. Just claim they do produce nasty weapons for groups that want the world see burn and install military at all their earth-bound installations.
Now your group of 300 is just a bunch of people sitting at the dark site of the moon. All they can do is playing space-chess with the 3rd-reich guys who happen to be their since the end of world war 2 ;) Well, in this case they would be the owners of that place, because they where there before any UN-resolutions regarding the ownership of space came in place :P
Okay, back to serious answering: Consider your renegade-scientists as a prime target for any nation with a considerable big budget for military. Sending a intelligent bomb (don't thing about the explosive agent... all it need to do is make a breach in their base' hull) up their if China, Russia or the USA (europe may have fallen apart until this date) get annoyed is something that any Kerbal Space Program Computer Player could accoomplish if he get the resurces... You could use an old soyus-capsule for accidential crahsing that building. Or laser them. Use them for railgun practice. Today technology isn't far from being able to reach targets this far.
And as said before: while its kind of save on the moon, they can't do much up their if their earth-bound facilities are hold by un-peacekeepers (speznaz, usmarines... I can't recall the china-troups name)... You get the point.
They need to hold something, the other nations are greedy for and not able to obtain to avoid such situations. Thats where we end up at He-3 which is said to be laying around at the moons surface and waiting for someone picking up it. And... yea, maybe you should read that 1400 page book. Or not.
EDIT: Or read @Thucydides answer, which I managed to completely miss. Seriously, this workplace isn't healthy for my observation ability :/
EDIT2: Something to take into account too: They won't have much research ability up there. Collecting moon dust and stones and process them might be something doable, looking into outer space too, but installing seriously powerful research equipment...
And don't forget about the communication. Using radio? Flood that site with radiowaves. Using an optical connection? Morse "who read this is dumb" in 200 languages with an earth-side laser and no one would be able to receive a clear message any more.
And even more: if you are trying to be something outside earth nation community, don't forget that your pirate scientists won't fall under any UN-law any more. Thats like a free pass for doing all that stuff that isn't part of any weapon or inter-nation resolution.
To be honest, I would not like to be part of such a installation, if there isn't any big guardian on earth... Oh, wait, we are part of the prime technology company? Wait, hasn't its posessions been sized by the financial part of the government because of taxation stuff?
But one thing there is that might work actually: prospectors right of claiming land. Whoever can make there a living and gather resources first is allowed to use this land (until the country decides otherwise). Something like this might work; just don't tell anyone you are building doomsday-devices up there.