You only need one ID and one proof of address (from the list of options you were given.)
You don't need to provide all of those proof of address papers.

As Rayna suggests, it should be easy to have a utility bill changed to include both names.
If you're struggling take a look at a bank account from HSBC. They have special account for new arrivals to UK. I know the account has a monthly fee but I'm not sure how long is the contract.

Sheldon, you really need to consider how to comply with the future ILR requirements for documentations of evidence of co-habitation. Either jointly or in individual names at the same address.
Get her name on as many documents as possible.

Just trying to help