Hi Alex,
As a BA Manager, I have to attend multiple meetings, all for different projects, so minutes are ley to me so that I can remember what was said and by who, what actions etc. I also happen to be a Master of ICSA (Institute of Company Secretaries and Administrators). Basically how to run a company according to the Institute of Company Directors here in the UK.
I don't think a solution needs to be designed. Its more a question of better practice.
In a meeting, you only need to note down something when a task is allocated or a decision is agreed. Everything else doesn't really matter so much.
So, during the meeting when you come to your first task being allocated or decision made, stop the conversation and ask everyone to confirm "Ok, so are we all agreed that John will take ownership of the database cleansing task and will report back next week?" (or whatever it is that you agreed).Lets assume everyone agrees that this is what was decided.
You therefore, write down in your notes "Everyone agreed that John would take ownership of the Database Cleansing task and report back next week." You add this to what you publish.
There are two reasons for doing this. One, it gives people a chance to reflect on what was agreed - was it really the best person to allocate the task to? Second, minutes of meeting can ALWAYS be challenged. Steve may say "Hang on, I didn't agree to this". That should also be documented.
To make things easier for you and the reader of your minutes use peoples initials. I have attached an example to this post.
Over time you will get better at writing notes and being involved in the call. You should also let everyone know who is what in the call - who is taking notes, who is chairing the meeting. Don't get the same person to be both. Although for small meetings yo may have to - it is best practice not to though.
Above all - keep it simple, to the point and don't over elaborate - you are only writing what has already been agreed, MInutes of Call 23072018a - example.docx
By the way, names etc in the example have been changed, Companies and people don't exist as far as I know, and if they do, its random luck.