I have 3 ideas about possible solutions.
1 If you know in advance that you'll have to explain something, you can try to prepare by doing "Half-Life Your Message" exercise (I learned about it & tried it yesterday, it's from Week 2 of a Coursera course, Foundational Skills for Communicating About Health https://www.coursera.org/learn/foundational-skills-communicating-health/) to find your "central message".
- Ideally, you first freewrite/brainstorm what you need to say.
- Now, set a timer. First, you try to fit your message into 60sec. Pause. Now set a timer for 30sec. Fit it in 30sec. Then do that for 15sec and then do that for 8sec. So, your whole cycle is 60-30-15-8sec, i.e. you go through halving the time.
- Now, write down that one sentence you got for the 8sec version. Is there any other thing you wanted to fit in? Can you incorporate it now into that 8sec version?
It's a really fun & intense experience, doing that exercise!
2 Also, you could read some concise but powerful fiction writers on a regular basis. Or good poetry. You become more concise & powerful in your speech through osmosis then. At least that's what was happening to me when I was doing those things…
And never ever read Dickens! :) I remember some years ago I used to be very concise in my written communications, then I happened to read his novel in several days, and found myself writing lengthy, wordy work emails for a few days after that. "Thank you", osmosis.
3 Since you mentioned that you worry that "things can be misinterpreted" — maybe read The Checklist Manifesto? It's an absorbing book — stories/examples from different industries about how well-constructed checklists can save lives (during surgeries), investments, buildings, airplanes. Checklists how-to are provided as quotes from industry specialists, somewhere in the middle of the book though… Maybe the book can give you ideas/mindset for communicating yourself more clearly but also concisely… It's definitely helped me to start making more concise & usable lists of guidelines for myself…