Try an Arms Reach bassinet. Hate to rain on the parade, but Moses baskets are considered a smothering risk. Arms Reach are the height of the bed, which will handle your boyfriend's complaint, and the side can be removed so the baby is literally at your arm's reach for nursing in the night. They have straps that attach them to the bed so there is no risk of a gap between bassinet and bed.
I had a moses basket and a bassinet that was on a stand. The bassinet stayed in the baby's room but I loved the moses basket because you could just move it around with you. Very handy and perfect for first baby AND second baby. You only use these things for like the first three months so best to not spend too much money on them in my opinion. I got my bassinet from my sister in law. Ask family and friends if anyone has one you can borrow---
But even though your boyfriend thinks the basket is too low, we loved it.
good luck