How do you keep a ruffled collar from flopping over?

Two layers of cotton is your problem. A proper Pierrot ruff is basially a fabric engineer project, and cotton alone will always slump because it's too heavy and too soft for the job. I've made a few of these for amateur pantomime stuff and the trick is fabric choice plus some hidden skeleton work. First, switch to tulle or stiff organza for the poof layers. A real ruff wants a LOT of fullness, like four or five times the neck circumference before gathering, and tulle gives you volume without weight. Keep one cotton or satin layer on top if you want it to look finished, but let the tulle do the structural work underneath. Gather each layer separately rather than sandwiching them, then stack them. It reads much fuller that way. For the support question, yes, you do want something in there, just not stiff wire all the way around. What worked for me was a narrow casing at the inner edge with millinery wire or even a couple of zip ties, plus a disc of buckram or heavy crinoline hidden between the layers sitting flat against the neck. That inner disc is what stops the whole thing collapsing inward onto your chest. Think of it like a hat brim hole with fabric exploding out of it. Skip starch entirely. You're right that it turns into a lampshade, and it also dies the moment anything gets humid. For attachment, snaps on a ruff are asking for trouble because the ruff pulls outward constantly. Best thing I've used is hooks and eyes at the back, two or three of them spaced along the inner edge, plus a band of non-roll elastic sewn into the inner seam that hugs the neck. The elastic takes the tension so the hooks are just holding position, not fighting the whole poof. Mine survived a whole show of physical comedy that way.

One last thing: hem or serge the tulle edges before gathering or it'll fray into fuzz after one wear.

The idea of using a buckram disc hidden in the casing to stop the ruff from collapsing inwards is exactly what I was thinking. For my own attempts at these types of collars, I found that adding a bit of thin plastic sheeting, like from a stiff shopping bag, inside that buckram circle really helped maintain the round shape. It offered a bit more rigidity without adding any noticeable weight. Also, when I placed the hooks and eyes about half an inch higher than the main seam, it seemed to keep the tension from pulling the collar off completely when I moved around.

I always found sizing the foundation tricky. Before I started sewing the actual fabric, I used a bicycle inner tube to measure the intended circumference. It helped me figure out that the gathers needed to be way more than I initially thought to get real volume. Without that initial measurement, I'd just end up with a stiff, disappointing hoop that looked nothing like what you want for the costume.

I was looking through your ideas and I am a little worried about the weight of all the poofy layers. If I put it on for a few hours during the party, will the thing feel too heavy and pull my neck down, making the whole thing look bad? Also, since you are dealing with so much volume, what sort of fabric do you use for the actual inside that touches your skin? I want it to be nice and comfortable, but I worry about it scratching me.