It's an interesting question.
I don't know the answer, but I am willing to pontificate on it.
I apologize for my longwindedness.
I should also note I am not a lawyer, do not take any of my ramblings as advice, seek actual legal council for a more concrete answer.
You are correct that a "concealable weapon" is defined as a firearm that is less than 12 inches, in Article 4 SECTION 23-31-210. Which defines the issuance of concealed weapons permits.
However, SECTION 16-23-10 defines a handgun for its provisions.
(1) "Handgun" means any firearm designed to expel a projectile and designed to be fired from the hand, but shall not include any firearm generally recognized or classified as an antique, curiosity, or collector's item, or any that does not fire fixed cartridges.
The relevant provision is
SECTION 16-23-20. Unlawful carrying of handgun; exceptions.
It is unlawful for anyone to carry about the person any handgun, whether concealed or not, except as follows, unless otherwise specifically prohibited by law:
(9) a person in a vehicle if the handgun is:
(a) secured in a closed glove compartment, closed console, closed trunk, or in a closed container secured by an integral fastener and transported in the luggage compartment of the vehicle; however, this item is not violated if the glove compartment, console, or trunk is opened in the presence of a law enforcement officer for the sole purpose of retrieving a driver's license, registration, or proof of insurance. If the person has been issued a concealed weapon permit pursuant to Article 4, Chapter 31, Title 23, then the person also may secure his weapon under a seat in a vehicle, or in any open or closed storage compartment within the vehicle's passenger compartment; or
So the law says a handgun (as defined in 16-23-10) concealed or not except as (9) states.
Item 9 (a) also never explicitly states a "concealed weapon", but uses the term "handgun" when referring to how one must store it.
Without a concealed weapons permit, anyone would be limited to the "glove compartment, closed console, closed trunk, or in a closed container secured by an integral fastener and transported in the luggage compartment of the vehicle" and that would include a handgun that passes the concealed weapon length limit. I see no issue here.
Now on to the more interesting part where I split hairs. The last sentence says if you have been issued a concealed weapon permit pursuant to Article 4, Chapter 31, Title 23 the you may secure your "
WEAPON under a seat in a vehicle, or in any open or closed storage compartment within the vehicle's passenger compartment"
Well, you have been issued a CWP pursuant to that section of law, it doesn't say that you can only place a concealable weapon pursuant to that section of law in those locations. Instead it only refers to the terms "handgun" and "weapon" as defined in this section of law (16-23-10) and "whether concealed or not" as stated in 16-23-20.
To me, that technically says it should not be an issue since it does not state that the handgun has to be concealable in the exception to this condition, only that you have a permit that allows you to conceal a concealable weapon.
If you contrast the wording of item 9 above to item 12, which grants the exception to allow people to get permits from SLED to conceal carry on their persons in public, you can see that in that language it explicitly states that you may only carry pursuant to the conditions set forth in the permit, which is Article 4, Chapter 31, Title 23. That language is noticeably absent in item 9.
(12) a person who is granted a permit under provision of law by the State Law Enforcement Division to carry a handgun about his person, under conditions set forth in the permit, and while transferring the handgun between the permittee's person and a location specified in item (9)