@Rachel Hunt - With respect to Holacracy, you may want a particular Role managing the volunteers so that they have to go through that person... You could also require x amount of notice that they will be coming over to volunteer or only in certain hours.
Whether in Holacracy or not, one thing you can do is have a written policy that you hand them or that you point to that they need to read or watch first. A lot of free online softwares even do this. For example, they remind people how many users are using the whole network, average response time to answer a request, that paid users will be triaged before free users, and they tell people to please be courteous and patient with the staff. They may even say to avoid using words that would be construed as "yelling" such as using all capital letters or underlining or !! and they may say something like these will be ignored or these can get your account terminated.
It can be helpful to remind volunteers that you completely appreciate their valuable help AND that in order to keep your doors open and continuing to give people good services, you need to prioritize certain paid work first.
The more you can sort of automate it by having clear simple instructions in writing or on video, the less staff time you might have to spend. It may not solve all the problems, but it should hopefully reduce the number of them.