We were already using Webpack + babel. Adding transpilation there is fairly inexpensive (done by babel, without type checking).
Type checking did roughly double our build time. Even then, we do run type checking during builds because we prefer the added safety even with this extra time.
Developers run with an incremental checking watcher. It does add a significant tax, and takes a few seconds after saving in some cases (3-4). We would love that delay to go away, but it is a cost we are more than willing to bear if the alternative is not having type checking at all.