I run no more than two cables, 12-2 or 14-2, through a 3/4" hole. Your 12-3 should be by itself passing through the stud, as another cable could cause binding and abrasion damage to the cable sheath. Multiple 3/4" holes through the center of the stud will not appreciably weaken it, as long as they're not close to a large knot or other cut, notch, split, etc. The common neutral configuration will not give you problems as long as the GFCI is downstream of where the neutral splits to two circuits. Bringing the wire through the drywall and cabinet frame into the fixture would be my choice, as long as the fixture is designed for romex connections.

I assume the wire you are running is in wall rated. Is the ceiling already drywalled? Can you access the ceiling joists from above (like from the attic)? As long as you can access the joists, it is no problem drilling and running a wire through joists. Even if you don't have direct access you can use a flexible drill bit to fish through joists as long as the run isn't too long and you know where any plumbing and ducts are. Here's an example of a flex bit. https://www.homedepot.com/p/Klein-Tools-3-8-in-x-72-in-Flex-Auger-Bit-53717/203871767 and a tutorial https://www.familyhandyman.com/electrical/wiring/fishing-electrical-wire-through-walls/ and check the suggestion of running conduit through base cabinets. Fishing wire through the joists is something I avoid (just me and my confidence/skill level) but it is fine to do, even if it can be challenging. If I have access to the joists, then no problem (just get in the attic and do it). It may be a longer run, but is it physically possible to run wire through wall all the way to the desired switch?

The type of lighting that is typically on its own switch includes pendant lights and over sink lights. This allows for more control over the lighting in specific areas of the kitchen. In terms of combining lights, you can consider combining the under cabinet lighting with the pot lights to provide overall ambient lighting in the kitchen. The pendant lights over the seated counter can be combined with the over sink light to create a focused task lighting area for food preparation or other activities at the counter. For the room size of 10'x16', having 6 pot lights should provide adequate lighting coverage. For outlet locations, it is recommended to have outlets installed along the countertops for convenient use of small appliances. Additionally, consider adding outlets near the seated counter for charging devices or using small appliances while seated. Be sure to follow local electrical codes and regulations when determining outlet locations.

acm: We will have "can lights" of a sort in the space, but as I said, they will be 11 feet up, and the ceiling is angled, so it will be wash lighting, not task lighting. We are specifically seeking light that will be able to be closer in and won't be able to be easily shadowed by heads, which is the benefit of under cabinet lights, ya know? jslazart, I was wondering about something like that coming off the side wall. Even thinking about something like this, this, which could be moved out of the way or directed as needed to where you are working, but wonder if it would look too busy: I have yet to see a kitchen quite like ours, but will see if I can grab a good angle of what I am working with in Google Sketch Up to show you what I am working with. Thanks for the responses!