Here are the images for overall kitchen layout and back wall of cabinetry

In the island behind the sink is a good spot because any garbage from sink just needs a turn and its in the trash!! Make sure you are leaving enough walkway between fridge and island. I cannot read on the plan what the distance is. And is that a doorway in the corner of the kitchen? Will that make your kitchen a walkway for everyone coming in from the back??

Mine is in the island behind the sink. I don't love it, but it doesn't really fit anywhere else (same reason as what you're noticing in your kitchen) and it's OK. In my previous house it was next to the sink which I think is ideal.

That is a small landing area to the garage and down the basement steps (behind fridge wall)
Distance between island and cabinets next to fridge is 47inches

I visited a friend who recently bought a house where the trash was behind the sink. I thought it was very inconvenient and sloppy. I think function should be first.

Sounds good.

I agree with more room to get into fridge. Especially if you have people walking in and out of garage and up and down the basement stairs.

If you can put trash beside sink, it would probably be best. I don't mind mine being behind the sink.

Our trash pullout has a "fake" drawer to continue the design of the drawer/door.

Probably out of the question, but have you thought about a pull out trash can under counter? Size is a limitation or course but a good pull out adjacent to the sink is ideal. If you're on a budget, you could leave the adjacent cabinet empty and install an aftermarket pullout, SimpleHuman makes some nice ones, both trash only and combo trash/recycling. The trash only bin is 8 gallons (if you're going by bag size, it's almost 40qt)

I know many people either have huge families/tend to generate a lot of trash and need a huge can, but we do just fine in our 3 person household with our 15 qt can. We recycle a lot, we smush everything that goes in the bin, and we empty the trash almost every 1-2 nights. Because the bags are so small it's easy to take it out any time. We also buy the simplehuman bags, which are virtually leakproof.

**edit: I didn't read your initial post carefully enough about symmetry. The simplehuman pullouts might be short enough to allow you to keep a drawer above.

I would keep the symmetric cabinets over moving the trash can. You will always need to wipe up the area around the trash can no matter where it is, so it would be easy to keep disinfectant wipes under the sink for when you need to swipe the cabinet or floor.