A system for controlling surge pressure in an oil or gas wellbore that is being drilled using a managed pressure drilling technique, the system comprising: a liner casing string and a drillpipe landing string adapted to be deployed into the well; auto-fill float equipment coupled to a lower end of the liner casing string and configured to allow fluid flow from the wellbore into the liner casing string as the liner casing string is lowered; a drillpipe diverter attached to the drill pipe landing string and comprising ports that, when open, provide a fluid flow path between an interior of the drillpipe landing string and an annulus defined between the drillpipe landing string and the wellbore; and a drillpipe flow restrictor attached to the drill pipe landing string above the diverter and configured to selectively block the flow path to the top of the drill pipe landing string while allowing fluid in the wellbore to be displaced up an interior of the liner casing string, through the ports of the diverter, and into the annulus defined between the drillpipe landing string and the wellbore, wherein the drillpipe flow restrictor is actuated to fully-open the passage through the drillpipe landing string and the drillpipe diverter is closed to provide a fluid flow path from the wellbore through the auto-fill float equipment of the liner casing string to a top surface while blocking flow through the ports of the diverter into the annulus; wherein the auto-fill float equipment is convertible to block fluid flow path from the wellbore into the liner casing string, while allowing fluid to flow from the liner casing string into the wellbore; and wherein the drillpipe flow restrictor comprises a drillpipe sub containing a flapper valve that is configured to block flow from a bottom side of the valve to a top side of the valve while allowing flow from the top side of the valve to the bottom side of the valve. a liner casing string and a drillpipe landing string adapted to be deployed into the well; auto-fill float equipment coupled to a lower end of the liner casing string and configured to allow fluid flow from the wellbore into the liner casing string as the liner casing string is lowered; a drillpipe diverter attached to the drill pipe landing string and comprising ports that, when open, provide a fluid flow path between an interior of the drillpipe landing string and an annulus defined between the drillpipe landing string and the wellbore; and a drillpipe flow restrictor attached to the drill pipe landing string above the diverter and configured to selectively block the flow path to the top of the drill pipe landing string while allowing fluid in the wellbore to be displaced up an interior of the liner casing string, through the ports of the diverter, and into the annulus defined between the drillpipe landing string and the wellbore, wherein the drillpipe flow restrictor is actuated to fully-open the passage through the drillpipe landing string and the drillpipe diverter is closed to provide a fluid flow path from the wellbore through the auto-fill float equipment of the liner casing string to a top surface while blocking flow through the ports of the diverter into the annulus; wherein the auto-fill float equipment is convertible to block fluid flow path from the wellbore into the liner casing string, while allowing fluid to flow from the liner casing string into the wellbore; and wherein the drillpipe flow restrictor comprises a drillpipe sub containing a flapper valve that is configured to block flow from a bottom side of the valve to a top side of the valve while allowing flow from the top side of the valve to the bottom side of the valve.