Integrated amp w/decent headphone out under $5k

Could use some help picking an integrated amp. Current Eastern Electric M520 24W EL34 doing a nice job driving my 95db efficient Omega CAMs. Would like to get to next level of tone and refinement and also drive my Hifiman HE1000 Stealth headphones (supposed to be easy to drive). Tried a SET separate but missed the bass definition and dynamics so I think I want to stay push/pull or warmer sounding solid state or hybrid. 10-25 watts should be plenty. Current leading candidate is LTA Z10… anything else I should look at?