My main motivation behind this post is to have my backup in two pieces to protect against a physical intrusion. A 24 word seed with higher entropy has no benefit over a 12 word seed if the physical backup is stolen. If I break the 24 word seed with 256 bits into two 12 word parts, can I safely store them in two separate locations like I can with the seed extension?
Of course you can store your extension separately from your seed, regardless of it's length or the origin of the words. As Leo mentioned above, it's actually recommended. If you want to, you can generate two 24-word seeds and store them separately.