Don't you have one with a slightly larger display?
Word order is quite flexible in Japanese. You could certainly move もう少し to be in front of 大きい to get ディスプレイがもう少し大きいのはありませんか, and it would not change the meaning.
もう少し大きいディスプレイのはありませんか is ungrammatical. ディスプレイ is already a noun so the の is redundant. If you remove の then you have something grammatical but you are asking a different question: "Don't you have a larger display". You would be asking for the display rather than the object that has a display (TV?).
However, I imagine that saying もう少し大きいディスプレイのはありませんか would mean: "Do you have a slightly smaller display?"
I can't understand why you would think this. It suggests that maybe there is something else about the sentence structure that is tripping you up. Perhaps you could explain further.
I also don't know what you mean by the 'extra が'. There is only one が in the sentence.
Edit to address comments
To reiterate, もう少し大きいディスプレイのはありませんか is not grammatical, and it cannot mean "Do you have a slightly smaller display?" To ask for a smaller display you would take your original sentence and replace 大きい with 小さい.
Now what about the が? I hope you will agree that ディスプレイが大きい means "the display is big" and that the が is an important part of this sentence and marks the subject of the sentence.
Now let us consider ディスプレイが大きいテレビ (A TV where the display is big). This is a relative clause. If you are not familiar with this concept then look it up (I think this concept may be the root cause of your confusion). Basically a noun can be described by the clause that precedes it. You see テレビ and ask "what kind of TV". The answer is "a TV where ディスプレイが大きい" i.e. "A TV where the display is big. 'where', 'whose' etc 'in which' and so on, do not have equivalent words in Japanese. They are handled by this relative clause concept.
Finally ディスプレイが大きいの works the same way as ディスプレイが大きいテレビ but instead of テレビ we have a special noun, の, that means "one", i.e. "the one where the display is big".