This is embarrassing. I just realized why, after so many years of studying Chinese, I still get 忙 and 忘 confused.
It's because they are the same character.
At least they are the same character to me: 心 radical and 亡 as the mnemonic. That makes them the same to my brain.
Now that I realize this I still won't be able to keep them separate, but at least I'll understand why I keep getting this hash collision.
Oddly enough, other characters with this property (e.g 景 vs 晾) doesn't confuse me at all. Maybe 晾 is rare enough and I managed to internalize 景 before I saw 晾. Neither does 裏 vs 裡; maybe because I think 裏 is a very awkward-looking character, too tall for its own good.