I like caloso's approach. Consider a road bike (10-11 speed, dropped handlebars, narrower tires) as a good bike and put wider tires with lower pressure on your hybrid. Aluminum (your hybrid, the Specialized Comp E3 and the Trek all are) tends to have a stiff, harsh ride. Both carbon fiber and steel less so. Now, going to dropped handlebars changes how you sit on the bike and can make bumps better at the seat but worse at the handlebars. CF forks (all of thise bikes) will help. Steel frames, especially ones of lighter, higher quality steels are well known as decent rides over rough roads and now there are decently light steel frames on bikes that are not expensive. They will not have the very light parking lot "wow" factor of carbon fiber, but many make really good all day rides, especially on roads that are less than perfect.

Seek out a good bike that can handle 28c tires. Good 28c's are barely slower than the very best and do wonders on lesser roads. My Peter Mooney, a moderately light all steel bike, currently sports Vittoria 28c G+ tires. Expensive, but the ride of dreams, even on very mediocre chip seal or old rural asphalt. (And not shabby whrn the pavement ends.)

You might look at "endurance" bikes. Now take that picture with you and if you find a steel bike that matches that "picture" and you like the ride, buy it! (It might not be new or cost a lot.)

Ben