I found the right post and followed the instructions:

* Accurate Texture Mapping (Off): Prevents inaccurate pixel rendering and icon sizes
* Normal Blender (Off): Fixes transparency in Link's hood as well as other rare object alpha glitches.
* Normal Color Combiner (Off): The default setting may be off, but if someone is unlucky to have 'accidentally' changed the default to otherwise, the game will look pretty messed up. That's what this option is for to back up.
* Primary Depth Hack (On): Fixes hard-to-notice polygon/textural glitches in the N logo at the very start of the ROM.
* Frame Buffer Emulation (Basic Framebuffer): Fixes background rendering when you press Start to pause the game. The setting with the smallest sacrifice of speed that still gets it to load.
* Rendering-to-Texture (Basic & Write Back): Smallest speed-costing option that lets you get away with fixing the rendering issue with Link's preview on the Equipment Subscreen.
(ulaoulao previous quote with instructions was for those who want to edit the ini file directly, the changes above are made in the graphics plugin configuration as "usual".)

However, this only partly solved my problem since the white rectangle was replaced with a garbled image. For me, the best solution (other than trying switching emulator) still is to run the game in 640x480 resolution.