It seems like the SOAP pull is only giving me the account code from the main line being replicated on the sub lines is there some other source that would have the correct account codes?

your answers remain consistent with whatever tool you are using retrieving records instead of search columns

So where would I find the other accounts? It must be available somewhere since the saved search shows correct accounts, the saved search does show the record type as invoice if that matters

do the search instead of retrieving records

I am a noob could you tell me search on which table and by what parameters?

start learning how to Define an Advanced Search