I used survey monkey to allow my players to give anonymous feedback about a year into my current campaign. (We're now in year 3.)
- I was running somewhat sandbox-y and had asked about if they felt they had enough direction to make meaningful choices.
- I asked if they felt they were getting more spotlight time.
- If they liked the speed of leveling or should it be faster/slower
- I gave a bunch of options (exploration, ethical dilemmas, spy, romance, intra-party conflict, action, diplomacy, combat, intrigue) and asked them to rate what they wanted to see more of and what they wanted to see less of.
- That campaign was 13th Age and I asked if two specific things were coming up enough (One Unique Thing which each character has, and icon relationships)
- And an open comments section.
Got good feedback. A lot more then I expected said they felt directionless, so I moved to more "structured" in that the players have clear choices of what to pursue, but what they go after or do is still all up to them.
The other categories were generally good, though each played had something that needed more focus. (One of them wasn't getting enough spotlight, another wanted that their One Unique Thing wasn't coming up enough, etc.)
I found they generally wanted more spying, action, romance, intra-party conflict, combat, diplomacy, and ethical dilemas, and less intrigue, combat, diplomacy, intra-party conflict, etherical dilemas, and romance. And they were getting just the right levels of ethical dilemmas, exploration, action, intrigue, diplomacy and spying. That part wasn't as successful as I had hoped - as a group they wanted basically more and less of everything, but don't change it because it's at the right spot.
Open comments gave me some more, such as it getting big, fast (turned into a travelouge where they were home based on a dwarven zeppelin and were at new locations instead of staying in one place and building up there and he was feeling kind of lost with few recurring NPCs and such. Another pointed out (correctly) that the irregular schedule was really a downer.
My suggestion is don't ask questions if you aren't willing to change based on the answers, and that might be tougher in the multi-GM environment you mentioned. The most useful part was to collect criticism so I can tailor more for my table and improve the game. But in some ways it was discouraging of "I thought they liked that" and "I put a lot of effort into that and they say I'm falling short". Ultimately it was very good to hear, but I needed to move past it as people being critical onto I had asked how to make it better and they told me, excellent!