The Missouri School of Mines (MSM) Spelunkers Club (based out of Rolla, Missouri) is probably the closest caving organization to you at about 1 hour and 38 minutes driving from Ellington to Rolla according to Google Maps driving directions. The Southeast Missouri (SEMO) Grotto (based out of Perryville, Missouri) is about a 1 hour and 55 minute drive from Ellington, Missouri according to Google Maps.
The SEMO Grotto is pretty active with cave surveying but I don't know about if they have many recreational cave trips that they do. The SEMO Grotto is based around where the longest caves in Missouri are. 4 out of 5 of the longest caves in Missouri are in Perry County, Missouri where Perryville is located. Crevice Cave (at 30 miles of surveyed passage), Moore Cave System (at 18 miles of surveyed passage), Mystery Cave System (at 16 miles of surveyed passage), and Rimstone River Cave (at 14 miles of surveyed passage) are all located in Perry County, Missouri.
Some great places to get some caving in are at regional and national caving events where many led cave trips are offered. The name of your region is known as the Missouri Valley Ozark Region (MVOR) so the name of the regional caving events in your region are known as the Spring MVOR and the Fall MVOR. The next regional caving event coming up in your region is the Fall MVOR which is being held next weekend from Friday, October 3rd to Sunday, October 5th which is being hosted by the Branson Area Tri-Lakes (BATL) Grotto based out of Branson, Missouri. The next national caving event happens to be located in Missouri. The national caving events are known as National Speleological Society (NSS) Conventions and the next one is being held in Waynesville, Pulaski County, Missouri from Monday, July 13th, 2015 to Friday, July 17th, 2015. The last NSS Convention that was held in Missouri was in 1997 so I would suggest that you take advantage of the NSS Convention being held in your state. There will be many led cave trips available at both caving events.
During the Spring MVOR, there will be cave trips available to McKee Cave, Saltpeter Cave, Skaggs Cave, Keyhole Cave, McKee #2 Cave, Rodent Scurry Cave, and Niche-Notch Cave.
And during the 2015 NSS Convention, there will be cave trips available to Carroll Cave, Skaggs Cave, Perkins Cave, Tunnel-Spring Cave, Grempeczynski Cave, Roubidoux Spring Cave, Roubidoux/Pike's Peak/Indian/Kraft Cave, Railroad Cave, Bridal Cave, Onondaga Cave, and Cathedral Cave.
And here are some links to information about caving in your area:http://nss2015.caves.org
(2015 NSS Convention)http://mvor.caves.org
(MVOR information including the upcoming Fall MVOR next weekend)https://orgsync.com/66617/chapter
(MSM Spelunkers Club)http://web.mst.edu/~spelunk/home.html
(MSM Spelunkers Club)https://www.facebook.com/groups/semoexplorers/
(SEMO Grotto Facebook Group)
I am sorry that I don't know of any caving organizations that are very close to you but I hope this information was helpful to you.