Or, if you want to try a longer trip than the ACA week long ones like I suggested above, but shorter than the cross country one, you could do the west coast of Oregon from Astoria down to California. Once in California, you do hit some narrow roads with almost no shoulder, but in Oregon you are either on a good road with at least a 3 foot wide shoulder or there are some short segments that the Oregon cycle map takes you on rarely traveled roads that are quite quiet and pleasant.
Contact Oregon and ask them for a copy of the Pacific Coast cycling map. I do not recall their web address, I googled it to find it.
I got a bit nervous on some of the bridges because some bridges did not have a shoulder like the rest of the road did, there were a few times that I waited on the side of the road until it looked like no traffic was coming for at least a half minute for me to get a good start across a bridge since I would be in the traffic lane on the bridge.
On the bridge below, I think that cyclists pushed a button to turn on the warning lights to warn traffic that a cyclist was on the bridge.
Then after riding the coast of Oregon, you should have more confidence about doing the trip.
The photo below is from Iceland. I only got nervous about lack of shoulder on Highway 1 which I avoided as much as possible because that was a very busy road, the secondary roads like in the photo below had no shoulders, but very little traffic and were quite safe.
I do not want to minimize the problems of traffic, I always wear a high vis jacket or jersey on busy roads and usually have my taillight in blink mode.
The photo below was in Canada, I think in Alberta, but I am not exactly sure where. Not much shoulder, but it was enough. And the lack of traffic made it pretty safe. This photo is from when I did the Glacier Waterton Loop with ACA, one of those week long trips I was mentioning.
With some more road time, you will develop some confidence and that will also give you an idea of the places where you want to be nervous too.