This argument is relatively clear-cut, but other real world arguments are more complicated.

I agree, but only because you include previously

If your objection to murder is predicated entirely upon the four reasons [emphasis mine]

However, most people would still condemn the silent murder of freindless, depressed homeless people, suggesting that they actully have more subtantial objections to murder. In which case this isn't a clear-cut case of TWAitW.