> Throwaway phone numbers are either caught and banned by spam filters, or present untenable security-risks to the account.

It seems like you might have already found your answer: establish a full-fledged bifurcated online identity. Instead of throwaway, create a bona fide secondary/tertiary/etc. number, email, and so on.

The challenge is that the networks are using these identifiers as both connection points and implicit proof of identity/existence. Throwaway/anonymous doesn't work well for the latter use case.