I'm looking into doing a variation of the Glacier protocol for cold storage (https://glacierprotocol.org/) using an Electrum multisig wallet. The main aspect I'm trying to replicate is setting up a 2 of 4 wallet with paper backups in different locations.

Once it is set up, if I needed to send some bitcoin I would restore one of the wallets and create an unsigned transaction from the multisig wallet. I could then travel to one of the other backups, restore that wallet, and then make the second signature. At that point I could transmit the transaction as soon as I get it to an online computer.

Here is my question: What data would I need in each location in order to completely restore the wallet and sign a transaction by visiting just two of the locations? I've created a 2 of 4 wallet while experimenting with Electrum, and for each copy (i.e. wallet 1, wallet 2, wallet 3, wallet 4) of the multisig wallet I needed the wallet seed and the master public keys of the other three wallets.

So, am I correct in assuming that these 4 pieces of information would be needed for each signing wallet to restore the multisig wallet?
Location 1: wallet seed 1, master pub key 2, master pub key 3, master pub key 4
Location 2: master pub key 1, wallet seed 2, master pub key 3, master pub key 4
Location 3: master pub key 1, master pub key 2, wallet seed 3, master pub key 4
Location 4: master pub key 1, master pub key 2, master pub key 3, wallet seed 4

Is there any additional information that would be needed at each location? Or is there any information I actually wouldn't need to store of the above?