@Soverihn yes that's very much on my mind, but I'm not at all sure what solution the international community would turn to, since it was seen to be quite a plum.
@Alex Richards With a POD in 1864, I'm not thinking a change in British colonial policy or events in the British sphere for some time...
@carlton_bach Apologies for the headache.
I should mention, I think, a bit more in broad strokes the European and in particular German background. I freely admit it is not the most rigorously plausible, but at the same time I am trying to not be implausible while still having a bit of a hand on the scales for a desired outcome (in particular, a milieu I enjoy exploring). The main conceit is a Wilhelm II who rebels to the left, rather than right, of his father, absent the influences of his grandfather and Bismark and their circle, and a conservative movement that, despite its strengthening by the unification wars, discredits itself soon after the Empire's formation. A path I came up with was, in response to a more liberal constitution for the German Empire (or even Empire of Germany*), and fears of a continuing erosion of conservative norms--and in particular, blame being foisted on Freidrich's wife and her malicious English influence--conservatives stage an "intervention" (I-can't-believe-it's-not-a-coup) to free Friedrich from said influence long enough for his Prussian good sense to prevail. It fails miserably, of course, and leads to Prince Wilhelm going missing, and then into hiding, for a week or so with the poorer sort, leaving a lasting impact on the impressionable young man. As you can see, a good bit of hand on the scales, but hopefully only on the outer end of the bell curve of plausibility, and from that (or from some other series of events) I hope to be rather more plausible.
*IOTL, as I understand it, the argument for German Empire and, in particular, for the office being German Emperor rather than Emperor of Germany, was threefold: first, it was to avoid tension with Austria; second, to avoid tension with the constituent states of the Reich; third, to avoid stirring up a more popular pan-Germanism that would be injurious to good conservative rule and to relations with Austria and the states. A question here is, given that (1) is not a concern and (3) is quite likely not as well, given the players involved at least on the Prussian side, is (2) enough to maintain the distinction between Nation and State when drawing up the constitution? Given, as you say, the tension and compromise involved OTL simply within the Reich, probably?
So, yes, a stronger left-liberal (and right-liberal, at least vs. conservative) influence on the early years of the Reich, although not an overwhelming one. A strong reason for my thinking it a pro-colonial government is as you say in an attempt to unite the fractious liberals, always rather too enamored of the joy of sects. Further, given the Manchesterish bent of (let us presume) the government, chartered companies strikes me as a very plausible route, with their inherent dangers and inefficiencies. I do, however, think that--for similar reasons to the Belgian government stepping in--Wilhelm II will feel compelled to (assuming he cannot be rid of them, that's at least anti-*this*-colonialism).
However, in regards to political Catholicism--that betrays another area of my ignorance, for I had thought that the struggle against political (and educational) Catholicism would if anything be fiercer, given that some of the strong support for that came from the left-liberals.
Regarding the basic constitution of the Reich, my thinking is that after Friedrich's death, given what new Kaiser they must suffer, even (or especially) the conservatives would support more power to the Reichstag vis-a-vis the Kaiser and the imperial bureaucracy. This might even be true before his death, since even without cartel backing they would have considerable support in the Reichstag and see that route as a way to check further crumbling of traditional Germany.
In terms of foreign relations, I agree entirely on a Franco-Austrian alliance; in fact, my thinking is that the alliance system will end up close to that of the Seven Years' War, with the addition of Italy and Japan on the Anglo-German side. My thinking here is this: After a slightly shorter and less brutal Franco-Prussian war (in particular, a lower incidence of francs-tireurs) Friedrich will attempt as best as possible rapprochement with France (eventually ending in failure, but not before appearing to have promise), including a smaller cession in Alsace-Lorraine and less ruinous treaty. Relations with Britain and Russia remain broadly cordial. With Austria hostile, much more effort is spent on Italy, both industrial investment and military missions.
Relations with Russia deteriorate through an Oriental Crisis (I am not sure if there even would be a Russo-Turkish war; if there is, it's not implausible it's a Turkish victory. Either way Germany is liable to back Russia even less than OTL. A further wildcard is if Alexander II is assassinated earlier...) before plunging to the depths on the accession of blustery, bellicose Wilhelm II (that part of his personality I do not think likely to change...), with him placing Germany, at least verbally, firmly on the side of Progress and against Reaction. An Austro-Russian alliance is not the most plausible of things, but if France could manage an Anglo-Russian one, I presume it can manage this, particularly with a worrying Germany in their midst. The Straits, though...
I do think this all ends in tear^H^H^H^H a Great War, of course, although as likely as not over Trieste or Warsaw or Strassburg as the Balkans (speaking of, a different or no Russo-Turkish war and that's also going to be unrecognizable).