I've now also figured out a solution to my first problem, though still not much of an idea of what really causes it. In drw_flush, after writing out the screen buffer, do this:

              push 0                        ; put X,Y offsets on stack
              sub rsp, 16                   ; 4 more dwords (don't care)
              mov eax, 16                   ; sys_ioctl
              mov edi, [drw_fbfd]
              mov esi, 0x4606               ; FBIOPAN_DISPLAY
              mov rdx, rsp                  ; ptr to structure on stack
              syscall
              add rsp, 24                   ; drop it
              ret

From what little documentation there is, this IOCTL takes a fb_var_screeninfo structure, but only pays attention to the x/y offset fields (so allocating 24 bytes for it should be enough). With the offsets set to zero, it now works perfectly on my machine.