Can you put the oven into the pantry stack? No reason (with some Ikea hacks of course) you can't keep food above and below an oven. Or perhaps a tall oven cabinet next to the dishwasher? You've got so much counter space it seems silly to bend for an oven!

some of the flaws are software-driven and some are because you haven't figured out your major zones and traffic flow yet. Using freehand kindergarten crayon sketches you could overcome both these flaws. This means I'm telling you to step back from the planning tools and focus on the big picture, broad strokes, area per area, general area, rough thinking. Many layout quandaries are worsened when people start using software (cabinet fantasizing software).

You have 52" aisle at your tightest spot facing the fridge door, so the other aisle space must be very wide. In some circumstances, aisles can be as little as 36", and 39", and 42", and when the aisle is slender one can enjoy pivoting or standing in the center and being able to reach to both counters, transferring things from one counter to the other. This is f.y.i.; my writing this out is not a recommendation to move your island over.

Since I cannot see your house, its normal traffic flow, I cannot comment about what to consider. Two doors are shown. Guess what they hide.

Do you have 30" to the right of the DW? Or can you make 30" in that area by putting the DW on the other side of the sink.? Are windows set in the wall or can they be moved? If you were able to put a full pantry also in that space to the right of the DW and include your oven in it then it might also give symmetry to the two walls by balancing out the bulk of the fridge on the end of the other wall.
Just a suggestion.
Does the island really have that funny cut-out corner or is that a software design issue.
If you wanted to expand (not move ) the island you could continue the leg that is towards the fridge another few inches to give you a 48" aisle. What is the aisle at the other leg going towards the sink?

The range seems rather far from the sink and rather close to the fridge. Does the sink really need to be way over there? I know sinks at the window are very common, but they're not obligatory. (Alternately, does the range need to be over on that wall?)

Also, you get an illogical flow with this setup. Most food that you cook comes from the fridge, but a lot of it needs to be washed or otherwise prepped near the sink (the trash is usually near the sink, so meat gets unwrapped and the wrappers thrown away, etc., over there). So a more logical flow would put the sink somewhere between fridge and range, instead of the range between fridge and sink as you have here.

What do you plan to use the island for? You could perhaps put the sink and trash pullout on the island, and then the range around the corner on the wall that currently holds the sink, to get the more logical flow. Of course, for that to work, you need to pay attention to Davidro's comment about not having humongous aisles.

Probably just not seeing it but, beyond the software issues, what is the advantage of the L shaped island? It looks like it is fighting the space.

My guess is that you don't want to move windows, doors, plumbing etc.
I would orient the island so that you have a long island facing the sink and the window. That way, the view from the island is through the window, which will be pleasing. Another option is to put a square shaped island, then you can sit on two sides of the island.

L shaped island does not look good, (IMHO) and it will not function well because you will be squeezed in the L.

I would move the sink to the left of the window as you look at it so the distance from the sink to frig is reduced.

Is your window drawn properly? That is a rather low from the ceiling window. Did there used to be soffits that you are taking out? If you are taking out the soffits and not raising/enlarging the windows, I think it will look odd. You may have to spend some money and raise the window appropriately....

I have a similar L with a center island. Frig/range then to sink. It actually works quite well for me. I don't need/want the water source on the island.

The skinny uppers next the hood does not cut it. It needs to be balanced with long horizontal shelves perhaps...

I have my speed oven mounted under the counter on the island. It works fine for me. This is not so popular here, however. Kitchen design is a balance of esthetics and function. What functions you accept may not suit another user. Pay attention to what functions/esthetics are important to you not what others think are important to you.

10 years ago, the rage was the two level island. I loved my 1 level island then and I would not budge from the position. Now, one level is more popular I also LOVE my island without a sink on it. Again, not a popular choice. But this works better for me.....

Another option for your kitchen, since it is so big is to fill the left side wall (where the frig is) with solid wall of cabinets/frig/pantry/wall oven. Then you have the island and 17 ft counter space to work with. This is a popular European plan. They often fill one of their walls completely.