AM is going away. FCC is moving the spectrum over to digital, A large portion of FM has already made the migration.
Unless something changed, when I last flew with an ADF (about 2014) it would not hold on a digital station.
In the scenario you present, I always play with the VOR when in cruise flight. All over the east coast I typically fly 5-9K with an occasional 3K or 11K just for variaty, and the whole time flying out west in May (roughly Dallas to Santa Fe to Cedar City to Provo to Omaha) I was able to pickup and maintain VORs. Out west I was flying VFR and way below the min nav altitude to avoid needing O2. I was often 3-6K AGL with a peak altitude of 11.5
I never had any issues with VOR. I could always find one to pick up. Was it the one that was direct on my route, nope. But I did get one.
In terms of the AM radio stations, they are very useless unless you know where the station is. Your better bet, get vectors from ATC.
Tim