Is there a clean and simple way to do this without damaging the edges?
tl;dr -- clipping path on a clone
- Begin with the object for which you'd like a shadow.
- Create a clone of it, and move the clone to the bottom.
- Apply a drop shadow filter to the clone. (You can adjust the settings of the drop shadow later through the Filter Editor.)
- Create a new shape where you'd like the shadow to be. This is your clipping path. For your case I'd recommend a rectangle whose bottom is aligned to the top of your main object. You can adjust this clipping path later if you like.
- Select the clone using Alt+click (to select below the main object) and then Shift+click to also select the clipping path too.
- Object > Clip > Set. (The one on top will clip the one on bottom.)
- Selecting the clipped clone object will now be somewhat tricky as you can't click on it. You can either draw your selection rectangle entirely around it (and subtract other objects inadvertently selected, if necessary) or use the XML editor to select it.
- To re-adjust the clipping path, select the clipped clone object and choose Object > Clip > Release. Make adjustments and then re-apply the clipping.