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Hello, my name is Richard and I will try to help you. Please remember I just report or interpret the law, so the outcome may not be what you hoped for.
Your BMI, etc licenses give you the right to play the music in public to an audience. However, since you want to alter the music, you would need to get the approval of the publisher of the works. BMI, etc do not have authority to give you permission to alter the songs in the manner you intend.
If you cannot get a response from the publisher of the works and so will not have the required permission, as a practical matter it is doubtful that anyone will notice the changes you made and pursue a copyright infringement case.
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If the Universal Publishing Group says that you can do it under their license, then I would not go any further in terms of seeking permission. You would not need a master use license because you are not doing that type of work. IF anyone complains just refer them to Universal Publishing Group. I do suggest you send the person you spoke to a confirming email so you have a record.