I wish I had a good suggestion. For me, baby #2 sleep through the night at 4-6 weeks, baby one was 4-6 months. They both slept in our room in a bassinet until they were at least 4 months old, it may have been longer. The first one had an amazing appetite, and still eats a huge amount and is nocturnal. He's now twelve and a half, 5'6 1/2", and 125 pounds. If allowed he will be up to 11-midnight and sleep to 11 am. The younger needed less food and slept better. Now, at nine, he sleeps so deeply he has bedwetting issues and has a BMI of 5. He rarely sleeps past 7:30, no matter how late his night.
It is so hard when you are sleep deprived and you have this person who for no rational reason is unhappy. I wish you the best. The only other suggestion I have that might work for you is one of those bed add-ons that gives the baby their own space, but still allows for co-sleeping.