Moma, I’m licensed in NY and agree that state ed. is a bit picky about what counts as engineering experience. We have some young engineers in our other offices who have run into the same problem as you.
I’d use specifics and avoid generalities. The details need to be about what you personally did and your personal contributions. They want to see a progression of experience, increasing in complexity and responsibility. (Not all work that you do will qualify as engineering experience either.) I’d avoid the general term “review” and use evaluate or ascertain instead. It also helps to be specific about what you’re evaluating something for, e.g., conformance with a particular standard like ASTM ??? or ANSI ???, specific design codes or regulatory standards, etc. Project management experience typically doesn’t count since a non-engineer can usually do this kind of stuff.
Just taking a look at your write-up, I don’t see any dates. State ed. likes to see precise dates of projects. Also, many of the items in here seem like they could be performed by non-engineers. I’d eliminate them or provide more specifics to better illustrate how they involve the use of engineering principles and judgement. When you talk about engineering calculations, I’d be more specific as to what kind. And honestly, some of the items don't quite make sense like "Reviewed contractor shop drawings to achieve contract drawings" which means precisely what?
Anyway, I hope this helps and best of luck with your application. It sounds like you already have some good experience. You may want to ask your boss about being assigned to some different projects to help broaden your experience.