There are more alternatives than I can count did you look elsewhere? For some reason people continue using JIRA and investing time and money on it. JIRA has an awful interface, is unnecessarily complicated, has a learning curve (when it shouldn't) and you actually need to know SQL in order to create helpful views for trivial things (e.g. have a proper view of hours/projects worked per week).
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A good practise is to request people (not just developers) to send a weekly email to manager(s). (Keep it concise AND bullet points MUST be understandable by anyone NOT familiar with their projects).
Major news: single line (if any)
Done: ...
Next week: ...
---And then. Have each team make a google doc. Write down goals/targets for the next month(s) and who's responsible for executing it.
Teams update the document once a month and email it company wide, open to comments.
I'd be happy to send you an invite for our private beta. Think of it as a blend between Slack and Jira.
If you can't do it with paper, you don't understand your process enough yet.
A manual process that is well understood can be well automated, an undefined process will struggle as automating something while also defining something always ends being a huge long project. If you can mentally model how to do it in trello, then do it, and come back to the automation step once you see it working (they have an API, you can get there).
Good luck!
Disclaimer: I am the founder of Odoo
I'm guessing you not talking strictly about organizing the tasks and projects themselves since there are a million tools for that.