Strategies to allow page-down or click under cursor-handle users to scroll without loss - if you must have fixed headers:
Don't put a background on the header if the header is widthed to 100%.
Design so that the header is left or right of the scrolling content (with or without a background colour).
Don't worry about the page-down or click under cursor handle inadequecies in browsers. It is difficult for a browser to take account of what is out of the flow when deciding non-manual scrolling.
Worry and solve by fixing the wrap that takes the content under the fixed header and auto overflowing it so that it has it's own scrollbars. Not too pretty! This illustrates the general idea