My point was that had TR accepted another nomination in 1908, the position of CJ would have become available in 1910 - and according to everything I've read, it would almost certainly have gone to Taft, thus removing him as a Presidential possibility. TR would have had to find some other heir to follow him in 1912. If Taft doesn't get the White House in 1908, he never gets it.
So unless you think Taft could be somehow re-elected in 1912 (wildely unlikely), I don't see how you could get a Taft Administration during WW1 - unless of course WW1 itself is moved forward, and the butterflies from that would be such that Taft instead of Wilson is the least of it.