the only way i can interpret "going deeper physically" is that you mean simply you want to be more flexible which in all honesty gives no sense of depth. stiffness is very very useful is you really want to intergrate your skeletal/muscular intelligence with an awaken energetic integration. integration occurs out of precise response to gravity and sensation. tightness and even injurys give a lot of immediate and precise feedback that helps to inform you how you need to move and engage. use the stiffness to find the proper spirals of the legs and an artful engagement of the bandhas. this will very much energize and nurish your practice. its the bandhas and how the inform the pose and breath that brings a sense of depth. not stiffness. stiffness is relative. everybody is stiff in yoga. but most people are not integrated. use the blessing of stiffness as your zen stick. let it teach you how to rightly use your legs, bandhas and breath. that is depth