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Selection of a power operational amplifier

Sorry to be so lazy, but I need a power operational amplifier.  I am looking at the ADA4870, LT1206, and the LT1010, but I am not confident in these selections (from a bandwidth perspective, they seem like overkill). 

Here are my specifications.

Input signal  (This can be changed if necessary):
Square wave ~ 5 volts peak to peak 50% duty cycle, all voltage is positive (bottom of square wave is at small millivolts) Frequency is 200 KHz (I would like it to work up to about 300KHz) These specs are feeding a 1kOhm resistance.  
Output signal desired: Single channel,  total of 4 watts, with a current of about 200 to 500 milliamps (so 8 to 20 vrms).  This feeds an impedance of about 400 ohms. I do not care very much about the signal integrity, including linearity, or shape of the voltage versus time trace. (It can be ugly, a bit of ringing, voltage spikes, or clipped, or close to a sine wave, or whatever.  This is for a novel transformer application)   I just need to preserve the major voltage change occurring at 200 KHz
Supply voltage desired:  12vdc single supply battery.
Efficiency desired:  Probably my biggest concern.  I'm hoping it can consume less than 1/2 watt (additional to the 4 watts being delivered to the output) under the conditions outlined here (so around 85 to 90%)..  It would be great to have an estimate of power consumption under the conditions described.  (I might be able to adjust my hopes.) 
Also, I am not averse to purchasing a dev board, if that speeds up my testing.  Please advise.  
It really needs to be readily available.  We have an order for 2000 units (that would include this part) that we are trying to fulfill within a couple months.  Im under a lot of pressure to get this out.
Thank you

Added a little more to the efficiency desired section. Added output voltage estimate.
[edited by: scstowell at 5:58 PM (GMT -4) on 18 Apr 2022]