I typed in "L shaped kitchens," selected houzz's "stories," and these resulted:

https://www.houzz.com/magazine/ideas-for-l-shaped-kitchens-stsetivw-vs~212920

--------------- https://www.houzz.com/magazine/how-to-make-the-most-of-your-l-shaped-kitchen-stsetivw-vs~61409645

No one is posting. In case this helps your process, here's an excerpt from the above article:

"With expert planning, an L-shaped kitchen will allow for an organized and efficient workflow. And because you can separate work zones in this layout, it can easily and comfortably accommodate you and another user simultaneously. In this respect, and also because they often open into a larger room, L-shaped layouts offer a sociable arrangement."

"Position wall units on the longer run. Again, it depends on where your windows are, but generally in an L-shaped kitchen with different-length runs, we would locate the upper cabinets above the longer run. This allows more wall storage compared with the shorter run. It also ensures glassware and cooking condiments are within easy reach of the cooktop below.
If there’s no window, you can continue your upper cabinets around the corner onto the shorter run, but often floating shelves or glass-front doors work better, as they create an airy, open feel. This gives the impression of a larger kitchen overall."

Firemans · More Info

"You can separate cooktop and sink. With a layout where both runs are roughly the same length, there’s usually space to separate the sink and cooktop on different runs. As the main prep space in a kitchen is typically between the sink and range, the benefit of separating these is that it makes this countertop area as generous as possible.
This arrangement also creates a distinction between your kitchen’s cook zone (with the range) and wash zone (with the sink), which facilitates efficient use of the space."

California Casual White Oaks Kitchen · More Info

I would vote to get the extra space for storage with the L, it will be a better flow and seem less disjointed. I think you'll quickly adapt to having to go around to take out the garbage as well. We designed our kitchen a few months ago and I was being picky about some stuff and now I'm really glad I went with the extra storage. You mentioned kids too, they'll quickly grow out of the running around the island stage and you can also give them the taking out the garbage chore if it annoys you to walk around!