With your approach, an attacker gets access to one sheet and they have 16 out of your 24 words. This gives them a significant advantage, as they only need to brute force the remaining 8 words. To brute force 8 words, they would need to check 2048^8 possibilities, and each possibility would require 2048 HMAC-SHA512 hashes as described here. This means an attacker would need to compute at maximum (2048^8)*2048 HMAC-SHA512 hashes to find your wallet. While this is still a very large number, it's nowhere near the security provided by 24 words. That's why we use 24-word seeds instead of 8-word seeds. Even though if the entire Bitcoin network was performing HMAC-SHA512 hashes instead of SHA256, and they were all searching for your wallet seed, it would take them around 1000 years (maximum) to find your seed, that's way way less than the security provided by 24 words.

You could do this much better by using Shamir's Secret Sharing. This would allow you to split up your seed into 3 pieces (or nearly as many as you like really) and require 2 (or more) pieces to put it back together. The best part about this is with SSS, an attacker having one or anywhere up to one less than the required number of pieces means nothing, as they don't know anything about your seed until they have all the required pieces.

You've got a good idea going, it could just use some improvement.