What do you think about running a parallel 2-two way road on both sides of the highway? They're a common thing in India and they intersect with the highway very naturally kinda like this:

https://preview.redd.it/3xbynln3vo0f1.png?width=1624&format=png&auto=webp&s=e0f49e986386051fa34e3ec9f9598813839dbd23

There's one on the other side also. It allows for shops, restuaurants etc. throughout the highway. They don't intersect with the highway much and most vehicles that want to enter the highway first need to enter the service lane (except when other highways intersect. They usually intersect with the highway directly)

Inspiration: the Grand Trunk Road