Your proposed use seems intended to add randomness. However, Schor's algorithm (for example) doesn't attack the randomness of a message but factors keys.

How would you propose to securely exchange the keys for the several algorithms? If there is enough meta or implied information for you to know what algorithms are used, an attacker would also know what algorithms are in use.

The obstacle isn't lack of randomness or an excess of decipherability but not using a quantum resistant algorithm.