A great deal of the joy of a
wood stove is
radiant heat, your plan sends all that lovely radiant heat into an essentially unused block house and reduces your
wood stove to the brutal inefficiencies of
convective heat.
The make a "wood furnace" that does exactly what you talk of, and ties into your existing circulation system, they are raging expensive...and horrific efficiencies attend, as they do with any convective system.
An outdoor boiler uses wood and at least heats the mass of water, water can be piped to a heat exchanger placed under the filter of your existing system and blown throughout the house, piped to wallboard (convective) units, sent to underfloor (or add on overfloor ) radiant piping, or piped through rock or
cob mass for radiant heat. an outdoor boiler can handle the burden of domestic water heating and relieve the heating burden of a clothes
dryer.
Finally if you have a "sliding glass door" could you create an alcove for your heater leaving your floor space unreduced you stove outside the structure, and still harvest the benefits of the radiant heat, the storage mass of the steel and firebrick, as well as lose the heatsink of a large expanse of glass?