Keep fridge as close to sink as you can for ease of off-loading and prepping foods under water.

I'll need some measurements to help you there, a floor plan sketch would be great but at the very least the length of the stove wall from the door to the end of the room and then the width of the opening into the kitchen

Don't make the frig fight with heat from the range ...I think your frig is too big for your kitchen. It would look most in balance between the window opposite it and the full wall cabinetry if that is staying there. Your dishwasher should be where the 'frig' apparently was/opposite the sink side it is on now. Your range can be in the center of the frig/range existing area, or more towards the den side of the kitchen, on the same wall it is on. Counter tops, and cabinets (with lower drawers ONLY) all the way around. Sink is okay where it is...

Here are some measurements my husband put into Ikea website.

Its a tight fit but I think if you put a 12" cabinet on the left side of the stove, then a 36" lazy suzan cabinet on the right turning into the peninsula it will work. Its a bit tighter than is ideal however the only other option is to have the stove right beside the door way which in my opinion is worse. Using those sizes you should have room for approximately a 12" overhang for an eating area at counter height. I wouldn't drop or raise the eating counter as it will feel tighter than it already is. You should have room for about a 60" long peninsula giving you ample space to walk in and out of the kitchen, but you could go up to 72" in length.

The eating area will be outside the kitchen a bit but if you get some stools without backs they can be tucked right under the overhang and completely out of the way when not in use.

At some point I would change the flooring to be the same throughout the whole house to keep the spaces feeling open and as one.

These are the two layouts we go back and forth on. Apologies - cabinet near stove wasn't cooperating on Ikea website so that's why it's not right up next to stove

Well for me the peninsula would end up being my prep space so I would probably do lazy suzan,, 1 or 2 drawer banks and a spice pull out with a knife block in it on the end (if that is an option, custom cabinetry company could do that but I have never worked with stock cabinets before so I'm unsure what all the options are) If spice pull isn't an option then I'd do all drawers or perhaps a trash/ recycle pull out on the end to keep people from going all the way back to your sink when they need the trash and getting in your way.