Gila

My shake at it:

He is an aging player. She wants to have a family with him, he does not wish to commit to such a "binding" situation - he is too busy socializing.

His socializing as a priority is reflected in, "Man you got a lot of jokes to tell, So, you throw your baby's banners down the well"(i.e. she is joking on his commitment to social engagement over what she deems as a more lasting "family" future they can have together)

His "handle on the past" is indirectly a statement of his fear of future commitment. Instead of progressing into life, this "he" chooses to rehash old behaviors as an avoidance tactic. "give a little more than you like" is a call to face his fear. These "little lovers" are younger lovers. Because he is older now, and his social appeal is rapidly shrinking, this can't last. This character’s irreversible fall from social grace is reflected in the "pick apart the past, you're not going back" statement.

She cares for him. So she is asking him to stop wasting time on the past. She is waiting for the "last ship to come in" - which is the last young girl to have an interest in this aging individual. A "kingdom half-mine" means she is only a portion of his life until he himself realizes that the younger generation no longer sees him as a "cool guy".

Finally, Gila may be a river, but the Gila is also a lizard. She is pointing to his aging skin and obvious loss of physical youth.

Don't hurt a woman's feelings; they get pretty bitter about that kind of stuff