So I successfully replaced UC6 and UC7 with MT42C4064-12 chips.  After all the soldering and desoldering, I was excited to hear the familiar chime after all was said and done, but was extremely disappointed that the problem persists.  In fact, I'm wondering if there might be multiple issues.  White or black pixels still track cursor and window movement on the screen, but there is also a lot of pixel flickering.  It kind of reminds me of "snow" on old analog TVs when a TV signal is weak.  The other strange thing is that this flickering matches hard drive activity.  So there seems to be an electrical issue somewhere.  Since I can't seem to upload video files, here is a Dropbox link to a video that shows what I'm seeing: https://www.dropbox.com/s/t92izeq7j80jzuu/se30_pixel_issues.mp4?dl=0

I have a working SE/30, and I see the problems when I install the board into either machine. 

Any help or suggestions are greatly appreciated!  My wife is wanting me to downsize my vintage computer collection, and I need to find a good home for this SE/30, but I'd like to get it working like new again, and not make this someone else's problem.