Maybe I should assign each iPad a unique identifier, and then perform some sort of lookup each time the iPad loads the layout?
Sounds like you need to set up Record Level Access control where each user's account name is used to limit which records they can access. See "Editing record access privileges" in FileMaker Help and check out this particular sub section: "Entering a formula for limiting access on a record-by-record basis" for a description of how to set this up.
There are a few options open to you depending on what you need to do ...
If you don't need the record to be edited after creation, make your list view open records in a non editable layout. A simple button could then direct you to another editable layout with GTRR to edit that record or create a new record.
If you only wanted each iPad to edit it's own records, then perhaps you can use the Get(username) function. The username is set in the FMGo settings under username and is different to the Get(AccountName) which is the authenticated account the user logged in under. However it is not secure and users can change the username setting. Anyway this can be assigned to a record when created and can be used to filter a list of records specific to that username or only allow edits if the current iPads Get(username) matches the created by Get(Username) which was populated at record creation.
Or as Phil suggests, the most secure method relying on privilege sets.
ps, Get(persistentID) returns a unique ID for each device if you really need to lock it down to the device, but then if a replacement device is introduced, it won't be able to access any previous records the device it replaced created.