If you value your SVS sub more than your BAK pre-amp, look for a pre that can drive a lower input impedance. EAR-Yoshino pre’s (tubed) are designed to drive a 600 ohm load (its designer, Tim de Paravicini, does work for clients in the pro recording field, in which 600 ohms is the standard). The EAR 868 includes two balanced/XLR pairs of outputs, and two unbalanced pairs on RCA’s, and has no trouble driving multiple low impedance inputs. Available in both line level-only (868L) and line level-plus phono (868PL) versions.
If you would prefer to keep the BAK pre, and want to keep your hookup at line level, another option is to look for a sub with a plate amp having a higher input impedance than that of the SVS. 22kHz is rather low.