We use our own tool https://zenkit.com for project management and it works great. You need one person who overlooks the tasks and reorganizes it when there is something wrong. The person organizing the Tech Team (like you) should know at least the basics of the technical stuff you use or what you (can) do. Is some info missing, you can just ask other persons via @mentions. At Zenkit there is a rule, that we need to answer to such mentions as fast as possible. The whole work becomes easier because you don´t need to call someone and you and the whole team can see what everyone is up to. For all these tasks we use the kanban view (like to-do, in progress, done) and many companies set a rule, that one person should only have for example three tasks assigned to him on to-do.