On the circuit I downloaded the resistors marked as R15 & R17 are grid stopper resistors to the push/pull output stage 6BL8's. There should not be a lot of audible difference between 4k7 or 10k however as they have recommended 10k resistors for stability then that is what you should preferably use.

FYI - In most EL84 push/pull circuits of similar design to the Lammington these grid stopper resistors can be anywhere from 2k7 to 15k however 10k is frequently used. Larger tubes like EL34's often have 4k7 or 5k6 grid stopper resistors. The exact final installed value is highly dependant on the applied DC plate voltage and current, idle cathode voltage and the tube load which is most often determined by the output transformer design and the connected speakers. Their main function is to limit grid current if ever there is excessive positive voltage applied to the output stage grid from the previous phase splitter stage. Instability often manifests itself as self oscillation of one or both of the output tubes, or alternately dramatically shortened life from either or both output tubes.