Having some issues with my island sink drain and I'm looking for some advice as I'm not sure what direction to go. The house is 18 years old and we have lived in it for the past 10 with little to no issues from this sink. A month or so ago we noticed that water would back up in the opposite sink bowl when running the garbage disposal so I figured that the drain line needed to be cleaned out after the holidays. Over the weekend we had a backup that wouldn't drain at all so I removed the trap and snaked the drain and all seemed well. Using the sink to wash hands, dishes, and such it drained great until I was cleaning up new years leftovers (sauerkraut) and it backed up on me again. This time I ran my 1/4" snake down the drain as far as it would reach, then I bought a longer 1/2" snake and cleaned all the way to the mainline in the house, where other plumbing connects and nothing else is having any issues. I then went to snake the vent and discovered that I don't have a standard vent as I do in the rest of the house, being an island it is what's called a "loop vent" or "foot vent", see the web diagram attached. I was able to run my 1/4" snake up an round the loop and back down to the drain so I believe it is clear. At this point I can take the 1/2" snake and push it all the way to the main drain in the house with very little effort, basically falls all the way down but I was able to still back up the line again by putting the rest of the leftovers (sauerkraut) in the garbage disposal. I removed the trap again and ran both snakes down the drain and the smaller one up through the loop again and water drains great, if I fill either bowl up with water using a stopper then drain it, it never backs up into the other bowl and drains quickly.

I don't know where to go from here, as I figured snaking the drain would completely resolve my issue. Some things that I think could be happening:

-There is still blockage in the drain even though I can push a 1/2" snake through it.

-The loop vent isn't supplying enough air behind the water when I have a lot of food going through it.

-The garbage disposal blades are dull and just not grinding up food as it should be.

I attached a picture of how my under the sink plumbing is set up as well for reference, any advice or suggestions would be greatly appreciated.