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Your total cabinet is 43.3" x 27.5" x 78.7". I used to run a 250W in a cab 36" x 22", with 24" distance from the bottom of the air-cooled hood, to the top of the hydro tubs the plants' individual 4" pots were sitting in. I ran 18 plants in a 6-plant rotation, pulling out 18-22" plants, averaging 1g per inch.. so 20g per plant on average. 4oz a month off a 250W hps. A 400W quite frankly would have been too much. But my space was a little smaller than yours. A 400 would probably do just fine. As long as it's air-cooled though. I needed to make my own hood though.. nothing would fit in a space so small.
Your space is slightly larger than my 4x2x(5ft high) tent. I use 400w hps/mh and heat isn't an issue, I do have good air and ambient temps are cool as I'm in a basement but 400w-600w is standard? for those med/small tents. Used to be, maybe that's all that was ever available that was worth a shit. Hps, mh....