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.
To me, the root of the problem is that most of the traffic leaving this junction is trying to follow the same initial path. The first thing to do is spread the traffic out a bit.
I think the easiest way to do this is probably to add more exits from your highway - since most of the cars leave the highway at this junction then turn right, it seems to be that you could add junctions "earlier" on the highway, which that traffic can then use instead of leaving here and doubling back.
The bridges either side of this junction seem like ideal locations, as do the bridges between Holly Heights and Olive Park. Basically, put exits from your highway everywhere where there's something for them to connect to.
About improving the junction. The easiest suggestion is to change the off ramp into the main traffic flow and make straight-on route use an off ramp - this seems to be how the traffic is using the junction after all - there's a quick example screenshot I've made below. If you try this make sure the highway has "straight on" arrows for all three lanes (not turn arrows) as show by the highlighted element.
The intention of this is to hopefully encourage traffic to use multiple lanes for longer, increasing effective density. However, notice how the highway joins to the 6-lane? With most of the lanes wasted turning left (because there's more lanes available that way), making this effort fruitless so far. You could fix this by upgrading the last bit of highway into a one-way 6-lane and reducing the existing one-way 6-lane to a long on-ramp (I doubt you have enough traffic going that way to need more). Ideally you should find a way to separate out your entrance and exits roads earlier.
This might not help as much as you would hope if all the cars still want to turn right at the first junction (which hopefully adding more exits should reduce). At this point you're stuck trying to optimise that single crossroads, which is not easy, but you could try some of the tricks with one way roads I discuss in my answer to the question you already linked to. However, to be honest, at that stage you're pretty much stuck.
Finally, the cars stuck in a loop. The game will despawn vehicles that it considers stuck after a while, meaning that it will dissipate over time by itself (assuming you've remove the source). You could remove a bit of the highway and let the traffic drive into the dead end to force them to despawn earlier.
Best Answer
The simplest, easiest and most compact way to connect the starting highway to a smaller main road is to just use a pair of one-way roads - one set from the incoming highway to the end of the main road, and one from the end of the main road to the outgoing highway.
This isn't necessarily the best junction, but it avoids traffic lights and allows uninterrupted flow of traffic on to and off of the highway - all for very little effort. I've found it to be sufficient for quite a long while after starting a city, I get much more traffic build up elsewhere first.
At the start of the game you cannot build additional highways, so for now you can use one-way 2-lane roads (see left image). This isn't great though - as well as looking a bit odd, the 2-lane road also has a lower speed limit than both the highway and six-line that it connects. It still works pretty well, but you should upgrade these links to use highway once you unlock them (see right image).
Highways at the top. 6-lane at the bottom.
2-lane version is left image. Highway version is right image.
Also, as a bonus, you can see an extra outbound highway link coming from the left for trucks leaving my industrial area.
Note how that merges with the other highway section in a way that doesn't interrupt traffic.
As said, this still isn't perfect. If you note the inbound road has a 'turn right' arrow in its right hand lane - which allows traffic to U-turn back onto the highway. In the highway version, this actually means only the left two of the three lanes will be used to merge.