Geez this sounds annoying for you and Brisco! Esp in the middle of the night. Grrrr.
If it were me, I would totally use counterconditioning to stop Brisco from barking back at the barking Rottie. If you make the noise predict happy stuff (yummy food and happy chat) your dog will probably not need to worry about the other dog. Hence the barking will cease.
We have a dog that lives behind us that barks at my dogs sometimes when we are in our yard. Originally my Gracie who was super reactive to ALL dogs (hell, all creatures!) would bark at any dog, esp if they were barking at her, scaring her. When this dog originally moved in and started barking at her, Gracie would run up to that fence area and get all riled up and bark wildly. So I started counterconditioning her to the other dog's barks.
Every time we heard neighbor dog bark, I got all happy, and said loudly "Hi doggie, how are you? Nice to hear you. You sound like a very nice doggie. Maybe we can meet sometime....etc etc"
My ultra happy tone sent the signal to my dogs that this other dog was NOT a threat, no need to worry or bark. Plus the neighbor dog heard me and would stop barking, since I sounded so happy and non threatening!!
And in the beginning, I would back this up with small yummy food bites as I counterconditioned the barking of neighbor dog! So neighbor dog barking= yummy food!
***I also use this method when training for reactivity on our walks and it is working wonders! Heck, today someone watched us as I asked Gracie happily "where's the doggie?" and she looked at the other dog (who was being reactive to her) and then right back at me for her praise & treat .....and then they asked me if I was a professional trainer
May take you a bit of time to teach your dog not to worry about the rottie, but it will be totally worth it. Heck you will be up anyway trying to quiet your dog, so why not use conterconditioning to create a happy association with the annoying noise?
This method totally worked for me and Gracie. I use counterconditioning for ALL triggers with her and my other dogs!