I find the OP’s ask a bit tough.
Finding a good DAC within an integrated is tough as many are an afterthought built to a cost.
Finding an integrated with HT past-through greatly limits choices also, seemingly eliminating low watt tube amplification which is typically matched with high efficiency speakers like Volti.
So the solution is likely a SS integrated, but maybe not ideal high-end Sonics vs other available integrates without the DAC+HT requirements.