Got it! Probably no one's really interested, so I won't go into all the details, but I started by changing from VBoxSVGA to the older VMSVGA virtual video card. Then I was again able to shift the installer window to the left enough to access the [Next] button and complete the installation.
After the installation was complete, I changed back to the VBoxSVGA support. Then after a lot of fussing with the settings in the Control Center, I was able to get MATE to full-screen, and the rest was easy.
Now it's fullly updated, and ready for some basic configuration. Just one more Solus edition to go, but that's Plasma, so it will be easy.