How to deal with large 4-gang switch boxes and the need to wire together numerous wires (>4)?

How many wires depends on the nut, and not just the color of the nut. I have red wire nuts that will only take 5 #14 and others that will take 6 #14 (don't recall the #12 numbers off the top of my head and the boxes are not here as I write.) The listed configurations are laid out in detail on the side of the box/container of wirenuts, and you don't get to be creative if a combination is not listed.

Looking on the website of the de-facto standard manufacturer in the US market (no affiliation other than I use them, and pay full price to do so): Ideal® Wing-nut reds are listed for 5 #12 - their plain Wire-nut reds are listed for 4 #12, the "B-Cap" variant is listed for 5 #12

In any case, if you have more to connect than your particular wire nuts are suited for, divide them up and then add a pigtail between them (which you don't have to count for box fill, but you DO have to count at each end for wire nut capacity.)

Yes, smart switches can be quite annoying like that! There are several ways to lick that problem.

Use a block connector that allows a lot of wires.

They make "stab blocks" that are a row of terminals, each with a "back stab". You jab the wire in, and it grabs it. They make these blocks to take up to 8 wires.

Or the MAC Block Connector: which has 2 larger holes, but each hole takes up to 4 wires. (It's intended for 1-4 copper wires to splice to 1-4 aluminum wires, but if you use them for all copper, I promise not to tell ;)

Now, since the smart-switch wires will be quite a bit smaller than the bulky #12 or #14, and may be too small to work properly in a stab or MAC Block, I suggest bringing all the smart-switch neutrals together on one wire nut, with a "pigtail" jumper to the group of heavier wires. You can easily nut four #18s to a #12.

Daisy chain wire nuts.

Your notion was to split the neutral wire to 2 or 3 "pigtails" then have each one go to another wire nut, which then ties to the various lamps and smart switches. That is perfectly fine, and a very logical way of thinking about it.

However, you can also "daisy chain": Join supply, lamp 1, lamp 2, and a pigtail to nut 2, which adds lamp 3, lamp 4, and a jumper to another pigtail, to nut 3 which has all the smart switches.

It would sure be nice if wire nuts took more than 4 wires! Now, first, with wire nuts, be aware of your "personal minimums". I have nuts that the book says absolutely max out at six #12. I've tried six #12, and let me tell you, no thanks. It's too twitchy, too hard to get right. And I'm good at wire nuts!!! I am more comfortable working with wire nuts in the "middle" of their range; so if the nut says 2-6 #12, I'll use it for 3, 4 or 5. (and go down or up a size for 2 or 6).

But second, yeah, shop around. They make all sorts of bigger nuts - the world doesn't stop at red nuts.