Ahhhh....I see better what you are talking about now. You're not alone. This is a common problem. Here is my method:
Whenever you can get away with it, do not use the "seam correcting" feature. This will give you a much more concise line which will be easier to "clone stamp" or "healing brush" in an app. like Photoshop (I don't know any other editing apps.).
The other option, that I seldom employ, is to use something like levels, curves, or brightness and a radial mask to reduce the light fall-off around the perimeter of the image circle.
I commonly deal with panos just like your example. My preference for fixing is to use the first method that I described. Even doing 3 pano stitches with Photovista or PTGui, I get the same sort of issues around the "poles" so, this is not limited to 2-hemisphere stitches.
You've already aknowledged your understanding of cropping the perimeter for better results. This is what the "Fisheye Parameter" adjustment is for in Panoweaver. Without cropping the perimeter, you can make some adjustments with this tool however (don't quote me on this one), it seems to be adjustable relative to incremental (not continual) differences in lighting. This seems to be why adjustments don't seem to make much sense when using this tool. What I mean is that the containing circle "jumps" rather than smoothly expanding and contracting.
When a photo has been cropped first using an image editor, try using the "Fisheye Paramter" then. You'll get no results from 0-100 because the image circle is too well defined for incremental adjustments. You'll get best results after cropping (to my experience) and there is no need to bother with the "Fisheye Parameter" settings. By not using the "Seam Correcting" feature, you will likely get a distinct line in areas of lighting difference or misalignment of the two hemispheres. For me, this line is easier to correct in an image editor than is a wide blurry area.
I hope I made sense, it's been a long day of work and classes. Let me know if something doesn't make sense to you.