I don't know if you had the chance to talk to Sean Drohan, who suggested to me via email to create a new admin account and see if Start10 showed its account picture correctly. It did:
Now, regarding my current account, I looked for those pictures and they were indeed not there. So I proceeded to convert my PNG account picture to BMP and stored a copy in C:\Users\YOURUSERNAME\AppData\Local\Temp\YOURUSERNAME.bmp and another in C:\Users\YOURUSERNAME\AppData\Local\Microsoft\User Account Pictures\user.bmp, as you suggested, and performed a reboot. And it worked! But here is where this gets interesting again: it only worked the 1st time I clicked on the Start10 menu. The 2nd time, it showed the black picture again, and it won't show my account picture again until reboot/re-logon.
So I promptly opened an explorer window to see if the pictures I had just copied were still there, and to my surprise they are, both in Local/Temp and in Local/Microsoft/User Account Pictures.
As I told Sean via email, this is a recent install of Windows and the only big recent update this system has seen is the anniversary update, but Start10 was working perfectly after that. And to be on the safe side, I ran the sfc /scannow command and that didn't help either.
I'm going to try and take a screen recording to illustrate this new issue I mentioned above.