Are you absolutely deadset on it representing a culture, though? Is representation what you're going for or are you working satire through your own perspective? Because honestly, it's totally impossible to give an accurate representation of ANYTHING beyond what we perceive (influences are vast, especially as we interact with one another more).
And I think that in the case of the spaghetti western idea, if you absolutely love it, if you're a fan, if you understand the tropes and a few of the socio-political/economic background for this genre, you can go wild! Love is first and foremost here, you gotta LOVE the concept, it'll bleed into your execution.
All that's really necessary is declaring that it's all your own personal spin on spaghetti western. It'd be so much fun for other fans to connect to points/gags/observations you make in your work based on what you've gotten out of it! That's what makes these old ideas fresh again, you know?