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

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.

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.)