I suspect the Pup could go faster if it had a different prop.
Perhaps, but the Pup has a web of bracing wires (although they were streamlined). The Dr.1 looks more modern in terms of design, which might give it a tad in speed. There are some NASA studies on these planes and the DR.1 has an unexpected drag efficiency.
Perhaps what might have made a difference back then for the Dr.1 was the climb rate, a more powerful engine and prop settings accordingly (plus the two machineguns). I know little about it, but Voss' prop seemed to be huge. That would give a decisive advantage for the Dr.1. Josef Jacobs liked his Dr.1 with a 130hp Clerget engine because of the extra punch it carried IIRC (and he flew them until the end of the war), so I think the Dr.1 would be a generation ahead of the Pup and pilots would not fear an encounter with the latter. Otherwise the Pup would not be replaced so fast and she would have the status of the Camel and the Dr.1. But we never know.
The community of private historic replicas owners could get together in some sort of historic institute to study those planes. It surprises me that especially the British aircraft don't have such a study with the whole royalty and proud of the country.