Overcoming Subleasing Clause in Lease with new San Francisco Regulation

How can I legally rent an apartment in San Francisco on Airbnb when my lease contains a consent-to-sublet clause?
Our new Short-Term Residential Rental Registry (http://www.sf-planning.org/index.aspx?page=4004#q03) contains this clause:

Important note for tenants: The Planning Department strongly recommends that you review your lease before submitting an application. The registration of your residential unit on the Short-Term Residential Rental Registry does not override any lease agreements, homeowner’s association bylaws, Covenants, Conditions & Restrictions (CC&Rs), or any other agreement, law, or regulations that prohibit subletting or use of your unit as a short-term residential rental.

My lease (like most others in the city I’d guess) contains a consent clause about subletting:

Tenant may not assign this agreement voluntarily or involuntarily nor sublet the who> le or any portion of the Premises without the prior written consent of Landlord., which consent shall not be unreasonably withheld.

This is described a bit more here: Topic No. 151: Subletting and Replacement of Roommates.

Has anyone had any experience asking their landlords for permission to do this properly?