I'm hoping to avoid memorizing a new seed phrase
You shouldn't memorize any seed phrase. Write it down on paper and keep it somewhere safe.
You are right, because writing the seed phrase down and document them as many they are will give a lesser problem for knowing or memorizing them, and if you think that you can memorised them you may skip some of the arrangement, I think it's quite understanding that writing your seed phrase on a paper should be the safest way of memorizing them because of long stays before making use of that particular wallet.