If you want to make this really work I would suggest you take advantage of your 9ft vertical height. This answer involves a ridonkulous amount of work but it is exactly what I would do in your cabinet (yes, 4 x 3 is a cabinet, not a room) and I have used this method before for very small 250w cabinets. Should work well for 1000 watts also.
Create a raised floor platform with particle board and polystyrene foam board. This raised floor will have 12” spaces between 2” x 6” support beams which are between the particle boards. The particle boards are sandwiched by foam boards.
The cross section of this raised floor is as follows: foam board , particle board, foam board, air gap, foam board, particle board, foam board.
Connect some galvanized vent adapters to feed the air gaps (through MERV 13 air filters) from a box which accepts the air filter and adapts to feed air into the void spaces of this raised floor. Make some holes in the floor (not too small to avoid excess frictio and not too few that you don’t equal the area of the intake vent) between where you plan on putting things.
Before making the vent holes in this raised plenum floor, make sure you could drill an equal amount of vent holes in another raised floor platform of exact size and construction. But this exact same platform is attached to the ceiling instead. This ceiling plenum with air gaps is fed through an equal amount of perforations as the floor platform and the air gap spaces act like air ducts which you will adapt to feed your carbon filter.
By doing this , you will have a true floor to ceiling air flow (completely vertical) which passes through the undersides of the leaves. This is how I ventilate small footprints. Heat rises naturally. Sure would be a good idea to make the air flow from bottom to top. Lots less friction when you do it like that.
You should also have more than one fan/filter for the sake of redundancy. Use a thermostat with probe cable to take outdoor temps and control (on/off not speed)the second fan when needed. Also, you need a 24VDC/VAC actuated damper on the intake register to control temps. Otherwise you have no real-time temp control. Some will tell you to put a fan speed control instead of an adjustable damper controlled by a thermostat and repeat cycle timer. But fan speed controls are not as reliable or effective as regulating the air intake through automatically adjustable dampers.
Did I mention that a fan speed controller will eventually break much much sooner than a damper actuator will?