掲示板 Forums - ませんか vs ましょうか

If I understand it correctly, using ませんか - it's like a tipical proposal question that invites a response.

with ましょうか - it looks like you are going to offer a solution and ask about it. like "May I help you?"

In the meaning that you can do an action to resolve the situation.

To add another perspective, ませんか is an invitation presented in a negative form, which weakens it in a sense.
Not too far from "would you like to"
ましょうか is more of a forceful invitational - "let's ?"
So I often see it as a ranking of how strongly you are asking the other person
weakest to strongest: ませんか、ましょうか、ましょう、よう.