How do I design an efficient exit from a large one-way road?

You could try a frontage road running parallel to your large one way

This allows for numerous entry and exit points to the highway without making a zillion intersections on your main avenue. The frontage road also "filters" the traffic to closer to where they actually want to go instead of having them all go in and out at the same place.

Here's a screenshot of one I made in game:

It's a bit goofy because I didn't have room to run on both sides of the highway but flows very well.

You need to spread this traffic out. This could involve building more entrances, moving this one, infinite roundabouts, forcing traffic in from another direction or something else. In terms of fast and easy fixes, you need to prevent cars following that single route and force them to spread out in some way. The easiest of which is by using one-way roads going against that flow. Note that with a patch that arrived yesterday you can now update between two-way and one-way road, so this is now easy to do!

Something like this (don't have the game on this machine so I've annotated your image):

^{red is one-way, blue is forced traffic direction}

Now the left 3 lanes of traffic on that junction will be able to go straight forward - hopefully traffic will start using more than the one lane, but that'll depend on the next junction. You could make both incoming roads one-way towards the junction, then all 6 lanes of the highway connection will be straight-forward. Or, you could also make all the roads at that junction one-way (so they cross, starting as the image above) - this would reduce the wait-time at the traffic lights.

Alternatively, if you make the side road they are aiming for into a one-way in the direction they're entering from, this will allow the right-most 2 lanes of its 6-way to turn right (instead of the current 1 - see how the middle lane is straight only at the moment) and you might get two-lanes then also turning left at the entrance. Whether or not this might work will depend on where the cars want to turn after that, but it might be worth a try:

Finally, you could make the side road they're aiming for into a one-way in the wrong direction, preventing cars from taking that direction. They might spread out depending on where other entrances are, but without know what the rest of that area looks like I can't say what effect that could have.