I see very little chance of Kellogg at this time. What foreign policy credentials he had came about when he was senator which started in 1916. The postwar Republican administrations emphasized domestic over foreign policy. Hughes does not have that luxury. He needs a heavyweight SoS.
Unless he intends to do like Wilson and be his
own SoS. Old Woodrow could never be accused of appointing heavyweights.
Knox would fit that bill. He is a bit hard to read re the war as you've noted. On the one hand he was recommended by Root so that suggests he is not too far apart but then he served under Taft, who was not in the Republican Warhawks camp and had his own idiosyncratic views about a postwar peacekeeping mechanism.
In a letter of Nov 27, 1915 to Lodge, TR criticises Knox for "defending Hypenated Americanism lately in a way which if persevered in will make him as undesirable as [Theodore F] Burton - - I did not think Knox had the proper understanding of our foreign questions - -". However, TR also states that he would "do my best to get the Progressives to support Knox if he were the man available - -".
"Hyphenated Americanism" as used by TR, was generally a euphemism for the views of German and Irish Americans. Burton was supported by many of the latter, so in TR's mouth that comparison was quite an insult. Yet in his desperation to get rid of Wilson, TR was evidently willing to swallow Knox and cross his fingers that he would make Root his SoS, which would apparently make everything ok.
This is pretty typical TR. Great man though he was, at times like this he reminds me of Toad of Toad Hall. His current obsession, whatever it might be, would drive all others out of his mind. Hence his absurd suggestion that the Progressives should nominate Lodge, who had probably never said a progressive word in his life, merely because Lodge happened to agree with TR on the latest bee in the latter's bonnet - getting into the war. All the reform issues he had fought for as the Progressive candidate had now become ancient history to him, and he blithely expected the party's "rank and file" to likewise forget them and troop to the polls as he directed. No wonder so many of them walked away and voted for Wilson instead.
Yet I still see a lot of Republican pressure esp. by Lodge and TR to pick Root and Hughes could be inclined to do this as a halfway measure to fend off demands for Teddy to have a direct role in his administration.
If I were Hughes I shouldn't (once the election was out of the way) have wasted time trying to appease Teddy. I suspect it would be futile.
My impression is thta the man had become temperamentally incapable of approving of any President other than himself. He fell out with Taft, so driving Taft out became his obsession - even though it made Wilson's election inevitable[1]. Once Wilson was in, getting
him out became priority#1, almost regardless of who got
in. Once Hughes was President, I fear it would only be a matter of time before TR found him, in turn, unacceptable for this or that reason.
[1] Or if not Wilson's, then that of Champ Clark or WJ Bryan, whom TR disliked even more. But as long as getting rid of Taft was his Big Issue, that didn't weigh with him