yup, I think you have it down exactly. Hybrids, (and mountain bikes) are usually designed to be built with flat bars, so they have a longer top tube. When a bar with a little more reach is added (usually a drop handlebar) you end up a lot more stretched out. A shorter stem will more the handlebars back in to position, similar to what you have on your road bike.

As far as handling, I've usually found the opposite, that more reach translates into slower (or more stable) handling. However, this is difficult to quantify, and it might just be 'new bike syndrome'. Changing the stem will definitely help fit though.