A tubing spool of a wellhead assembly can include a body having a body cavity, a first channel, and a second channel disposed therein, where the body cavity is configured to receive a tubing hanger used to couple to and suspend a tubing string, where the first channel is configured to be in communication with a tubing string cavity within the tubing string, where the second channel is configured to be in communication with an annulus located between the tubing string and a production casing, and where the first channel and the second channel are each configured to facilitate flow of at least one of a plurality of fluids in either direction independently of each other. The tubing spool can also include a first back pressure valve disposed within the first channel and a second back pressure valve disposed within the second channel.