An interesting concept. I'd recommend single piece metal discs, other materials would likely shatter, split or be too unpredictable. You're main problem is limiting the kinetic energy of the weapons and if you go back to basic equations you are therefore either limiting the moment of inertia or the rotational velocity. Rotational velocity is relatively easy to limit however MOI is a bit more tricky.

I'd set yourself a limit of say 500J or 1000J of kinetic energy then work backwords from the worst case disc design to determine the max dimensions and weight of said disc.

As mentioned earlier this may be safer with middleweight sized machines. Audience wouldn't be able to tell the difference and the forces involved are likely to be smaller.

You're roof is gonna be the problem area but as it doesn't have to be see-through would it be possible to throw a few mm of a cheap impact resistant plastic such as HDPE of the top of your current netting?

Velcro armour? Good idea!

I'm watching with interest as I wouldn't mind building a bigger spinner at some point and knowing me, I'll try and push it right to the limits for fun