To answer this, it helps to look at the personality of Behrmen. O. Henry paints him to be a rather gruff, sarcastic man who is a bit rude and surly in his attitudes and behaviors towards Johnsy and Sue. However, he does hold a fondness for them; he helps to pose for their paintings, and has established enough of a relationship with them to be a confidant for Sue when Johnsy gets ill. O. Henry writes,
"He was a fierce little old man, who scoffed terribly at softness in any one, and who regarded himself as especial mastiff-in-waiting to protect the two young artists in the studio above."
So, despite his fierceness, he cared for the two women above and considered himself their protecter; this is evidenced in his apparent sacrifice and effort to paint the leaf on the wall in the bitter cold. His heart is soft and sacrificing.
If Behrman were to tell the story, he would probably focus quite a bit on his failed masterpiece, his love for gin, the silliness of the two girls above him in the building, and on the ridiculous fancies of the sick Johnsy. When Sue tells him of Johnsy's fixation on the leaf, he openly shouts and laughs at the silliness of it all. But then, have him go down to his apartment and start worrying about Johnsy. Have him take one last drink then head out to do his work. We might then get his last words before he dies, which might focus on the silly girls above, his fondness for his masterpiece, and the ridiculousness of his position. All of these perspectives would fit in well with the personality of the unexpectedly kind-hearted Behrman. I hope that helps; good luck!