The refrigerator is much too far from the main work area.

That and, yes, you do have a good bit of wasted space between the kitchen and the family room on the "no table side".

I'd like the sink to be more centralized. The dishwasher is going to be far from the cabinets where you're going to keep your dishes. Lots of steps. I'd say switch it with the stove, but that gives you a window-issue.

Could you "turn" the kitchen one notch counter-clockwise? I mean, make the open end of the U face the sliding glass door side? That'd allow you to have the open area in front of the door . . . and you could have the table in the corner. Or, you could build in a great banquette in the corner. Yes, the door to the mudroom is a problem, but you could make the pantry a walk-through connector from the mudroom to the kitchen.

Perhaps you could extend the island towards the nook and actually have it with a table attached to it. It would give you more space by your patio doors and eliminate the dead space. Below are a couple pictures I found that have tables attached to islands but not necessarily with the island in the right direction. Your aisles look very generous on each side of the island, if they are perhaps you could shrink them a little and make the island a little longer. If put a drawer stack in the island facing the dishwasher, you could just pivot and put dishes in the drawers. I do think you should move the refrigerator closer to the working area of the kitchen, perhaps next to the pantry. You might also want to consider putting a prep sink near the pantry/ fridge end of the island.
This first picture is GW's deb52899
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This one is GW's annekendos's :
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Here are a couple more (don't know whose)
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Or something like this without the wine fridge:
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Here are a couple more island with table pictures
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Is there some reason why you don't have windows on the west wall (as drawn)?

I read part of your building a home post - enough to try to help by stating that the OP entertains frequently for family - but family is 30. And the dining room is narrow/small - it seems to be something like 10 x 16.

It would be nice to know:
--- How many people are cooking in that kitchen daily? How many people eat a normal meal?
--- If the big family groups normally are just major holidays, or monthly or weekly ...
--- What kinda stuff y'all make? Daily bakers, do canning or other special activities?
--- How are you guys when working together? I don't like it, personally - I have always wanted a complete second kitchen for family members ;) But lots of people love to prep together.
--- How often do y'all eat or cook outside?
--- Do you cope with serving the large numbers? Buffet? Serve at table? Pass service dishes?

I don't say this often, but that kitchen is really big. It doesn't have a layout suitable for multiple cooks or large scale entertaining that isn't catered. That second part may or may not matter to you.

These are littlish things while waiting. Don't think this is a plan - its just a collection of ideas.

I would try out cleanup combined with beverage bar where the refs are drawn. That would put the main dish cleaning/storage where its accessible from both dining areas AND ALSO give a second sink that could be used by extra cooks or people doing cleaning tasks while others are still working away. In addition, it could give a sink/counter space for drinks service during entertaining. I would also consider adding ref drawers as the final bit on the east end of that run - it makes the drinks, ice, etc. very accessible to people so they don't have to cross into the business end of the kitchen at all. A dedicated ref frees up some room the "real" ref from having to store a lot of bottles, cans and what-ev-var.

Maybe try removing the cabinets on the north wall completely? Little bit more open feeling having a "L" with island vs. a "U".

Put a sink in the island - think about eliminating the stools and perhaps making the island a little less long, but fatter? The island top could be like 39" by maybe 60-65"? Perhaps a little rounded to accommodate people working closely together?

It provides a more direct entry from the garage, moves the guest closet into the mudroom - which grew a bit and the kitchen got smaller. The family room ALSO got a little smaller due to poaching for the cleanup run. Would get architect dude to reformat the ceiling and move the slider. Paired the slider for no reason whatsoever.

The mudroom got larger. The dining room got a little bigger - think it could push out a little more - adding to to 3 feet to dining room.

Same basic plan, but another version would be just to go ahead and make the pantry really big - from the west wall to the lockers.

Just as an alternate to the attached to island tables, you could also just have a rectangular table and place it where ever its convenient for you. I would be tempted to reverse the use of the dining room and family room - or to make the family room into a dining room with a couple of comfy chairs and make the dining room into an office or a movie palace. I've always had a crush on formal dining in the kitchen.

Or you could have a bench attached to the island and then use a table with chairs in front of the bench. This would allow you to have an expandable table for more seating when needed. Something like these pictures
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Or this with a table in front
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Or this with the island on the backside of bench
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With it where you've written in the "R," the fridge would be in a fine location if you added a prep sink to the bottom left corner of the island. I think a prep sink would be almost a must in a kitchen this size, and a layout this spread out.

I think your aisles look big.. Meaning I think your island could be larger. If you wanted to, you could arch the overhang into the 'dead space' to utilize it more.

Turn the chairs at the round table into an X formation instead of a +, and that will give you more room to access the door. This does seem like a good opportunity to have one of those islands with table seating attached, although that limits the use of the island as work space from all sides.

Concerns: I don't see dish storage near the clean up area. I wouldn't use a diagonal corner upper to the left of the sink, especially since there are no cabinets on the sink wall. Those work better as a connector, and look odd with cabinets only on one side. I would run the cabinets straight to the sink wall in that corner.