Well, while the standard compact ACOG was designed to be mounted on a carry handle, there is no reason but the default base to mount it on a carry handle because none of the compact ACOGs have BDC ladders.
With that being said, since you already have a TA31, getting another ACOG, albeit a compact one, will allow you to train with the BAC on both rifles or train twice as much if both optics are going on the same rifle.
However some people are never as fast with a BAC-equipped ACOG as they are with a red dot at close range (50 yds or less). It should also be noted that some people are highly effective within 100 yds with a TA-31 though most feel that the chevron reticule is not quite as fast within 100 yds as the donut reticule. The lower magnification of the 2X model may make using BAC at close ranges easier for you.
As far as the ML3 goes, it's a great optic for the ranges you're looking to use it within and beyond. The only thing you really lose is good target identification at longer ranges. Then again, I don't know if that matters to you or not.
So in the end, based upon what you have and what you're considering purchasing, any of the optics you mentioned may work for you. It all depends on you really.