How to transfer garbage from the full landfills to the incinerators

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.

I haven't found any (official) evidence to prove my hypothesis following now, so be aware that it might be wrong.

You say that you have no industrial zones at all. So, let's check this chart first:

You see that there's a production chain which requires specialized and generic industry to create goods for your commercial buildings. If you had that, you could easily lower the import rate. However, you don't have those buildings or zones so basically you import everything. You can read here too that offices are a clean alternative to industry, nevertheless they don't produce any goods.

• First off, there could be an unknown import cap. Really unlikely, but possible.
• As stated here, import trucks, ships or trains don't use the nearest entrance to your city. They spawn wherever they want to. So some trucks could be already on their way, however, they're taking ages since they have to drive through your whole city. That, too, would explain why some ships just have cargo of 50%. Maybe there are still boats on the sea coming from the bottom end of your map to your upper end. In the meanwhile, other ships spawned recognized that they don't need 100% cargo because other ships already have the cargo.
• Also, do your commercial buildings import at all? Stated here again, some buildings not connected to any industrial area nearby do most likely not import stuff.

I guess the whole problem is that you miss industrial areas. Your problem isn't well documented nor reported because it doesn't occur that often. Most cities have industrial areas, you and few others don't have them and are suddenly facing the problems of too less goods. As you can also see here, offices have some downsides:

• Fewer jobs.
• No goods.
• Less commercial tax income.

As a fellow city builder, I can just recommend you to build up some industry. The flow will be way better and less troublesome. Yes, you have pollution. Just be a dirty (real life) mayor and hide anything negative from your citizens by placing it far away from them and covering it up.

As said in the beginning, I don't have any official evidence supporting my hypothesis, but I hope I could still help you with it.