So you are talking theoratictly and I am saying what happened when I raises the value 10 mW. Why inSSIDer showed the invrease of 4 dBm after the change in TX settings coould be either because the value was changed or just Asus own firmware doing the change. The environment was the same , the distance the same ...
Other factors can influence perceived RSSI, including client and antenna position, obstructions, humidity, etc. Was the reading consistent, or did it bounce all over, and the 4dBm increase was the peak increase?
The folks here who have spoken out about reciprocal power are correct. There's little point in going to 500mW if your clients can't return that sort of power. Most mobile devices hang out closer to the 50mW or less range with antennas that aren't capable of more than 2-4dBi gain.
WiFi is a two-way communication. If your client can receive signal from a "really loud" AP, but can't transmit at a point where the AP can receive at similar RSSI, you're accomplishing very little except for creating a frustrating experience.
Now, if you're attempting to bridge two routers with an equal transmit level, you'd be far better off equipping the devices with a highly directional yagi style antenna and using a lower transmit power. The antenna gain will take care of the rest without distorting the signal, and you'll be equally capable of reciprocating the signal at the far end. Plus, you'll be far less likely to violate any regulations or piss off your neighbors.
That all said, I agree that specialized equipment to handle the distance (appropriate antennas and amplifiers) is a better approach if you're attempting a long-range bridge. Using multiple APs is a better approach if you're simply trying to provide better coverage in a larger building. In either case, a single ASUS router is likely not the right tool for the job.
Perhaps if you explain what your use case is, the folks here can provide a bit more guidance to help you achieve your goal.