Of the three Native American bows I have been able to look at closely, two were definitely ash, and probably green ash (Fraxinus pennsylvanicus), both of which were sinewed. Neither one was over 40 inches and both were in pretty rough shape and no one even suggested trying to brace them. Sadly, the owner of these two bows will not let White Eyes touch them or even look at them anymore, so I cannot get photos or even measurements even though I have full respect for the history and culture.
The third one looks to me to be chokecherry and is also sinewed and it appears in the Museum of the Fur Trade in Chadron Nebraska. Sinew backed, recurve/decurve, painted, about 50" (if I remember right), with several arrows and full provenance of where it came from, when, etc.
Back to ash and sinew. If you are wanting to recreate a known technology and be historically correct to a certain tribe in a certain place and time, I would give you a hearty thumbs up for the combo. But if you are looking to build one bow with sinew backing that you can count on day after day for years to come, then I would point you at yew, osage, or another bow wood combination that resists compression failure. Having said that, I am going to sinew an ash bow this fall and leave another osage unbacked.