Mike, I tested having 6 lines in the report header, and in Report Viewer I see all 6 (just as in your browser screen shot), but when I exported it to Excel, only the top 5 lines show.
I found a workaround, but it is NOT dynamic, and you would probably have to play with it to get it "just right" for your needs.
Anyway here goes: I copied the 5 header lines to a blank worksheet, and added the 6th line below. Next, I centered the text in the column, and then turned off the gridlines. (View > Show > Gridlines).
Then I took a screen shot of the text & saved it as an image. (I used .bmp, but MR also supports .jpg & .png)
Next, delete all of the lines in the 'Second section' of the headers, then click in the first line of the second section & then click on the Images button (to the right of the 'Insert Auto Text' button) and select your image.
Two things I found when doing this:
1) In Report Viewer the header looks perfect, but when I exported it to Excel the image was very narrow.
2) You can only enter Text or an Image in one header section, not both.
The second point is important, because as I mentioned earlier, an image isn't dynamic, and at least from what I can see, you have the report date in the 6th line.
My suggestion would be to maybe abbreviate some of the text & try to combine two lines into one.
Or if possible put one of the lines in one of the other header (or footer) sections, if it make sense to present it that way.
P.S. FWIW I tested in Excel & was able to enter eleven header lines. (I stopped at eleven because, well who needs THAT many, and I like Stranger Things!)
I'd like to hear how you decide to move forward with this limitation.