Just got back to this forum post now Job, apologies.
One avenue, which you may need technical assistance from someone you trust is to crack your own seed phrase. As you said there are 1024 options for this last missing word of the 12, sadly because you don’t know which position/order it is in this may make it difficult.
Get someone you trust that can code python - tell them to create script that locally creates private keys for each of the of the 1024 options in position 12. The export of this script should be all those private keys for your 11 words + 1024 options for position 12.
Then create another script that imports each private key in a wallet, syncs it with the blockchain, and returns a value or string to you if there is any balance in the wallet. Run the 1024 options for position 12. Then consider if you want to do that for all the other positions in the seed phrase (for example word 6).
This will take some time, and you should probably pay the person making your script or give them a % reward if it works. Really depends how much LTC you are talking about.