Hi Joshjo,
As per your requirement, I understand that there is no change in Transaction type. If yes, you just need to extend new bank accounts (along with Bank Key) to Transaction Types which is already in use. Please go to t-code OT83 and maintain the configuration there.
Also, you are right about new house bank. The bank account needs to assign to new house bank t-code FI12) and then you can link that bank account to EBS setting as described above.
Once the configuration is done, you need to inform bank with the details of new bank accounts so that they can send MT940 with updated record. After it, you can test the file through standard EBS transaction FF_5.
Regards,
Gaurav