To kill the screen latency, you could use Miracast, which seems to be much faster than the chromecast (see https://www.youtube.com/watch?v=J-5JJhKMph8) or connect a cable (best solution: no heat because of the video encoding, can recharge the phone with MHL, no lag). Also one issue would be the DPI. Working with the big android elements on a, say, 24 inch screen would be a pain. But maybe you could automate a DPI change to rescale the whole interface.
Bluetooth keyboard and mouse, of course, already on the desk. Chromecast hooked up to the monitor. Use one of the Android automation apps to automatically mirror the display via Chromecast when the phone is in range of the BT keyboard / mouse on your desk and when it is laying flat on a surface (plopped onto the desk).
Not perfect. Chromecast latency might be an issue. You would still have to plug it into a charger if you don't have wireless charging. But it should work.