I would suggest tilting your Brooks saddle up slightly more and try that. Sometimes, if the saddle is flat, you tend to slip forward, and may compensate by tensing your back muscles. If you look at the Brooks saddles of many people who have had them for a while, you will see that there is a definite upward tilt of the nose.

Be aware that a longer stem that encourages you to lean further forward may also compromise the position of the Brooks saddle. If you already have it tilted up, it will likely put extra pressure on the perineum area. If it remains flat, the stem may solve the issue, but then you might spend money on a stem for no good reason.