The phrasing seems very slightly different than natural (for a native English speaker).
For example: "2003, the twin elevator changed the industry. Two cabins, independently in one shaft."
To me, it's just slightly weird to say "independently" without a specific action. It reads like what the cabins are doing independently is... just being. I think a native speaker would be more likely to say, "Two cabins moving independently in one shaft." Then the adverb has a verb to modify.
For example: "2003, the twin elevator changed the industry. Two cabins, independently in one shaft."
To me, it's just slightly weird to say "independently" without a specific action. It reads like what the cabins are doing independently is... just being. I think a native speaker would be more likely to say, "Two cabins moving independently in one shaft." Then the adverb has a verb to modify.