I'm still struggling to understand why you need something other than the currently available plain text encryption options. This really does seem like reinventing the wheel to me...
One reason is I'm not familiar with other encryption that I can print, but another reason is that anything non-standard makes recovery more difficult years later. I (or someone else) may not remember exactly what was used.
Is it because you want wallets to provide built in methods to encode/decode the mnemonic string?
That would be my preferred solution.
Turning the result into another mnemonic string sounds like it should be possible... but then, why not just use the original seed and a strong BIP39 passphrase? Surely this ends up effectively resulting in the same thing... a mnemonic string + passphrase?

BIP39 passwords are relatively easy to brute-force. I like how BIP38 is several orders of magnitude more difficult, which means the password itself can be easier to remember for many years.
That's pretty amazing, the problem there is that software you mentioned is for linux. I would need a windows tool that could do the same type of thing.
Sorry, I can't help you there. You could search for the source code, but setting up a Linux system is probably easier.