Proper grammar is important, but sometimes grammar checkers and proofreading aren’t enough.
If you aren’t sure about a preferred phrasing, try using Google to see what’s popular.
When you Google both phrases, “sitting at the drawing board” gives you thousands of more results.
That’s your tip that this is the preferred usagejust be sure to put the entire phrase in quotes.
How to Use Google in the Most Unusual Way to Make Your Self-Editing Faster, and Better| Problogger.net