"We had a similar problem at a bluegrass festival with just 5000 people, 4 different free WiFi access points, all unusable because connections timed out due to being so overloaded."
4 access points for 5000 people? Yeah your gonna have a bad time. Most access points can support like 100 people on them max. In a temporary situation, I would have gotten at least 10, more like 20 APs for that amount of people and a wireless lan controller to manage them. We regularly use aprox 80 APs to cover a building with 5000 users. You completely underestimated how many APs you need for sure! I never covered a large outdoor space, but you usually do these things by number of people attending because each AP can only handle so many connections.
Stadiums on the other hand sometimes have thousands to tens of thousands of APs and as other people pointed out, concerts in those stadiums work ok. Someone also said that the wireless infrastructure was provided just for the benches (or whatever they are called). So the surfaces would have had thier own wireless network on the playfield. This makes sense as no one is going to use the same wifi network for public as for something as important as team tools.
Having used MS surface devices professionally, I can say that they are nice, but they are also quite buggy, so i would blame them and windows 10 for most of the problems. Bring some ipads in and see if they have the same problems, i bet they dont.