Hello, and welcome. I am a licensed attorney and happy to assist.
This is quite a situation. I'm happy to say, you hold all the cards. You are correct in that a partition action can only be brought by a co-owner. Since this organization simply leased the land from you, it has no standing to bring a partition action. The land is yours, and that is that.
As for ownership of the two buildings, I have more good news. Unless otherwise in writing, when a tenant affixes anything to leased land, it immediately becomes the property of the landowner. A fixture is anything that cannot readily be picked up and moved, and buildings certainly qualify. All parts of each structure are yours, though things like desks and shelving not permanently affixed to the building belongs to the tenant. That is the law.
I hope this helps. If you need additional information or clarification, just let me know and I'll continue to provide assistance. If I have addressed your issue and/or pointed you in a positive direction, please let me know that, as well. Also, please remember to leave a positive rating when prompted, as that is the only way attorneys on this site are credited for the help we provide.