"I assume that the same logic applies in the US that the busier routes are contoured more gently given that they are designed for freight to use and cannot have excessively severe gradients, whereas some of the quieter back roads are more likely to have the severe climbs."
Well, maybe. If I were you, I would assume nothing about the roads here in the East that I might be using until I had researched them.
(1) Here's an example. I have not biked this but have driven it. I-68 runs east-west across WV and MD. It also carries the designation of US 40. I-68 replaced Old US 40. Old US 40 stills exists and in many places parallels I-68 just a few hundred feet away. US 40 is the old National Road route that in various incarnations goes back to about the 1820s. Old US 40 was THE main route through this area before I-68 replaced it. I-68 has the 3% gradients you are talking about. Old US 40 is a roller-coaster of endless up-and-down rollers. Riding rollers like these all day is more demanding than you might think. And this is a main road of its day.
(2) Many of these main roads would be state or US highways. However, many of them have a shoulder no wider than 2 feet or less, or no shoulder at all. Here in PA, PennDOT is gradually putting shoulders on state roads as it does major reconstruction on them, but the majority of the roads haven't been done. If you want your bike trip to be a memorable adventure, just wait till you have 18-wheel semis with trailers and their accompaning wind drafts go by you at 50-60 mph 2 or 3 feet from you -- I guarantee it will be.
I would suggest you consider some combination of the following:
(1) Get online and at some topographical map sites and study the maps covering your routes. Some sites charge, some don't. From the maps you can get the elevation gain and from the map scale some idea of the distance of the climb, and roughly calculate the gradient of the hills.
(2)Also for state highways, most states through their DOT website have traffic volume maps of state highways so you can get some idea of how much traffic is on a given road.
(3)You might consider buying a topo mapping program like DeLorme's Topo 8.0. It will allow you to experiment laying out your own routes. It will also give an elevation profile for the mapped route. You drag the mouse over the profile and it will give you a running gradient. Some of these gradient numbers will seem fanciful in the course of running the mouse over the slope, but you can still calculate an average gradient based on the distance and elevation gain.
I hope you will see this and consider aozolins and my advice to plan this part of your ride carefully. Good planning lets you know in advance about issues like this one, so you aren't surprised. Bad planning does not. You've got two people who live and bike in the region telling you that this ain't easy, dude. A word to the wise...