Your on the right track thinking about using exhaust gas as a supplement for the garden but not with ANY furnace,even with a modern 95 percent efficient furnace the ppm of toxic gasses is way too high to chance in an occupied dwelling.
My line of work affords me the use of air monotoring gear where ive found out for myself that even the cleanest burning furnace or boiler is too dangerous to use.
What you can use is a gas or propane fired water heater & run the exhaust vent into your room,just be damm sure that the exhaust pipe going from the heater has enough rise to allow the exhaust to flow & not become vapor locked within the pipe.
Ive ran both my main room using the exhaust from my natural gas fired water for over 3 years straight with excellent results in bud production vs straight non supplemented air,i estimate an easy 10 % increase in overall bud production which in a room your size will add up into lb's.
Ive been chastized by the nay sayers & the doomsday police on this site for giving this advice in the past, not to mention being threatened with an infraction from fdd for giving dangerous advice but it is what it is ,the system works great & poses very little danger to life.
It works great for me.