No mention here of Rev War service: http://archive.org/stream/bairdbeardfamili1918catc#page/172/mode/2up
Also the reference cited above has a large number of discrepancies, for example Bedent, Obediah, and Barzilla are all nephews of the Zebulon Baird that died in 1804.
Given the dates, I would suspect Zebulon was more likely active in the French and Indian War (1754-1763)
Different birth date date, but I think this is your Zeb: http://services.dar.org/public/dar_research/search_adb/?action=full&p_id=A004842
There are 44 Bairds in the DAR database. You can search for them from their public search engine: http://services.dar.org/public/dar_research/search/.