I like your outlook. It’s certainly possible. Just getting a healthy Wilson and Pierre-Paul back on the field would be a huge boost to the offense and defense, respectively. But I wouldn’t call it a “key over free agency.” I think the improvements you list above are a complement to what the Giants did in free agency this offseason. Or, since the Giants ideally prefer to build through the draft, their free agent additions complement the hoped-for contributions of recent drafts you outlined. If the new players perform as well as the Giants anticipate and the players you cited step up their games, the Giants should be significantly improved.
I know that Hynoski and Connor are good fullbacks and we will have to cut a good player by the start of the regular season, but what is keeping the Giants from using Hillis as a fullback? I know they have tried using Pascoe as a backup, but teams usually like to get as many weapons on the field at the same time. Why not let Hillis play some snaps at goal line or short-yardage fullback?
In this case, position designations are moot. Peyton Hillis did carry the ball in short-yardage and goal line situations. When he does so, it doesn’t matter whether he’s called a running back or fullback. The Giants would like to get Hillis, a bigger back, running behind a fullback in such situations. I imagine the same will be true for Rashad Jennings. But as far as Hillis lining up at fullback, the Giants don’t view him playing there, especially since they have two good players competing at the position.