Greeting.
The Persians in AoE2 already span possibly the widest historical age range in AoE2, with their UU and UTs being based on the Sassanid Empire starting in 224 AD. They don’t need to also represent the Parthians who predated them and who would be more appropriate as a civ in AoE1.
Of course with the options available in the scenario editor, you can feel free to make the changes you suggested, and you can even rename the civ to create your Parthians. I’m doing something similar with a Goth origins campaign I’m making that includes the Sarmatians (similar to Parthians).