] Perhaps he really believes, and I would be inclined to agree with him, that in the present climate of the play, he is better fit to be king.

I would agree that Claudius is better King material than Hamlet, at the moment. But Claudius believed he would make a better king and therefore military leader, than his brother, else he would not have killed him (among other reasons).

But, just how good a military leader is he, really? Fortinbras is demanding the return of the lands King Hamlet won, and is gathering an army in the cause. Claudius rightly tries to put an end to this by writing to old Norway. So far, so good.

But what happens when his ambassadors return? Norway reigns in Fortinbras who obeys him

Whereon old Norway, overcome with joy,
Gives him three thousand crowns in annual fee,
And his commission to employ those soldiers,
So levied as before, against the Polack:
With an entreaty, herein further shown,
That it might please you to give quiet pass
Through your dominions for this enterprise,
On such regards of safety and allowance
As therein are set down.

So, let me see..... someone who wishes to wage war against Denmark, gathers an army to do so, saying that they are off to fight the Polack as a cover, promises not to fight Denmark, is given more money for his army if promises to wage war on the Polack, but, darn it, he has to cross through Denmark to get there, so, that's ok, right?

Now, I am no military strategist, but it seems a no-brainer that you don't let someone who has threatened war against you to travel through your land with an army! But Claudius' reaction? "It likes us well;"