The kanji 網 and 綱 are both said to be composed of the same two radicals, 糸 and 岡, but this is misleading because the kanji are not also the same. Instead, 網 should be said to be made of 糸, 一, 冂, 丷, and 亡 to prevent these easily mixed up kanji from being more easily mixed up.
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I’m not Tofugu, but based on ideas they share here, which you can also find discussed in, for example, Remembering the Kanji, I think five radicals is more radicals than is ideal.
If I needed more help distinguishing the two kanji, I might consider whether some combination of those four alternates you suggested is worth becoming a radical for my personal use, and following WK’s methods make up a story and a name for it.
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I wouldn’t mind if they made a new radical for it, but I think interpreting it as five existing radicals is a more realistic approach. It may not be ideal, but sometimes, there’s no other way.
懲 is also said to be made of five radicals, although the four on top make up 徴, a separate kanji. They also state this in the mnemonic. I’d also be okay with that approach for 網, combined with the five radical interpretation, so long as they also differentiate 罔 from 岡.
It’s always a bit rough with those components that are barely used anywhere else.
At least as long as 亡 is recognized as a part of 網 it should be a good compromise.
亡 罔 惘 網 魍 is a phonetic series with readings ボウ・モウ.
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Seconding a request for a more careful treatment by the content team for these two. I’m certainly struggling with retaining and differentiating them.