Textbook-RSA meet-in-the-middle attack against other RSA based schemes?
I suspect that the meet-in-the-middle attack you have in mind is what is presented in this answer (or something similar).

If so, then it's not actually correct to say "the only requirement is that the message be a product of 2 numbers of the same magnitude"; the message needs to be a product of two numbers of the same small magnitude.

For example, the attack can work if the message were a product of two 64 bit numbers; however this would imply that the message itself was no longer than 128 bits.

This is a credible attack against textbook RSA used to pass 128 bit messages; however any sane public key encryption method (such as ISO 18033-2) would include padding to make the message presented to the RSA primitive much larger; this completely invalidates this attack.