Good feedback so far. Now for more questions.
First of all, if the POD involves the Americans losing their war for independence, would it be possible for them to rebel again and successfully gain independence on their second try?
It's absolutely possible, and that, indeed, was part of the scenario I proposed. However, it would probably be a more nationalistic and centralised American state, due to the longer and bloodier struggle for independence; it would probably not be called the 'United States', which was an explicitly federal move. A much tighter federation is likely, maybe even an outright unitary republic. But the anti-British backlash will deliver the same libertarianism as existed IOTL, and 'manifest destiny' will still happen (probably even more strongly due to the longer period of British power keeping the Americans away from the Appalachians), thus leaving an American culture fairly comparable to OTL's.
That does, however, presume that the British do nothing to mollify the Americans' concerns, e.g. lifting the Proclamation Line or devolving tax revenue; neither of those outcomes are impossible in the much more decentralised British colonial empire that existed before 1776. So I would judge that a successful American rebellion after this PoD is possible, but not certain.
The reason why I ask is because I've been wanting to have the United States play some role in this timeline, with a Walt Disney-like President in power from the end of WWII to the 1960s. Basically, someone who would have been known for their work in art and film, and as President would have been credited with bring America onto the world stage while at the same time detracted for his length of time in office and as being a "dictator with a smile".
For Walt Disney himself? Impossible. Even an 1870s-era PoD is going to leave Walt Disney butterflied out of existence, and by that time Germany and Russia are too close to OTL to realistically switch roles; a PoD in the 18th century will mean he can never exist.
For someone like him? It would depend on the development of American culture, but all the most basic elements that created OTL's American culture (libertarianism and mistrust of government, strong religiosity, probably a civil war over slavery, expansion at the expense of the Native Americans and 'manifest destiny', and frontier spirit) are still there, I think. Perhaps someone who's studied the social history of the USA could comment on this.
Second, what territory might an Austrian-dominated, unified, and expanded Holy Roman Empire control? Are we talking Lebensraum-sized portions of territory, or something the size of the German Empire and Austria-Hungary put together, with some other bits put in?
Certainly not Lebensraum-sized portions of territory; for that Russian power would have to be decisively broken, and history has proven that that is very difficult to accomplish. This is hard to answer, because it's pretty implausible for the Holy Roman Empire of the German Nation to survive anyway. It would certainly include the Habsburg domains and eastern Germany. Whether it would get what IOTL is western Germany, I don't know; it depends on the progress of future wars, as the Kingdom of France will be interested in claiming much of that.
A useful force to awaken German nationalism would be an invasion by the Kingdom of France. If that happens, and if France is successfully defeated by the HREGN and its allies (almost certainly including the British and maybe the Spanish and the Dutch too if the French are being very expansionist) that might unite all of the German-speaking lands under the HREGN, and such a large and powerful HREGN is probably needed, since we want it to be big enough to survive against a super-Russia (as any industrialised Russia would be, compared to OTL).
So let's say that when Great Britain loses its war to a European coalition in the late 18th century, the rest of Europe manages to secure major victories over the Royal Navy, thus permitting a French invasion of Great Britain that turns southern England into a French puppet kingdom while the United Kingdom of Great Britain retains power in the rest of the island of Great Britain. As a result, the rump UK is essentially unable to resist France, for fear of invasion; this nicely neutralises the British threat that would cause problems for my scenario later. Later, a Louis XIV-style charismatic soldier-king gets the throne of France sometime in the 1810s-1830s, determined to make France the hegemon of Europe. The Kingdom of France tries to expand at the expense of the Dutch Republic and the western-German petty states that are nominally part of the HREGN, and succeeds, beating off Spanish attempts to stop them. Then the French invade the bits of the HREGN that are actually under solid Austrian control, they get over-extended and they're thrown back; they don't have the resources of OTL's Napoleonic France, with its conscription and efficiency at providing vast armies for the Emperor.
That would unite all of the German-speaking lands, maybe even the Netherlands too, within the HREGN. The HREGN would also keep the parts of Poland that went IOTL to Austria and Prussia, and it would have the territory of OTL's Austria-Hungary. Later, it would probably forge an alliance with the Russian Empire against the Ottoman Empire, since the factors that make Russia desire to expand against the Ottomans are already in place and the HREGN in this scenario is a natural ally against Ottoman rule.
Third, would butterflies from a 1776 POD diverge things enough to allow neopaganism to become popular among the extreme-right? With the Ultra-traditionalists, or Puchoviks, as I've called my Russian Nazi-analogues, I want them to be so traditionalistic that they would consider the Abrahamic faiths unfit for their ideal Russian state, labelling them "Jewish lies and superstitions", and have an ultimate goal in removing the Orthodox church and replacing it with their take on revitalized Slavic paganism, which they would consider more legitimate for a unified Pan-Slavic state.
It would be difficult for a *fascist movement to start off opposing Christianity; Christianity was very deeply rooted in Russia just as in most of the rest of Europe. Any fascist movement that takes power basically has to accommodate Christianity, since such movements depend on fear of radical ideologies that ordinary citizens view as a threat (such as communism), and any fascism that calls for the end of Christianity will be considered a great threat to the ordinary values of small-c conservative *Russian families who might otherwise support it.
Maybe if a *fascist movement gets a lot of power in Russia it might, once it is already securely in power, act against Christianity—but even that is difficult to imagine, given that the *fascist movement's support base will be in small-c conservative families who enjoy the security of a traditionalist movement and feel threatened by radical ideas.
I'll also be adding a link to a Google Docs sheet where I'll be setting up a rough timeline based on input from you all. It might be wiser for me to make this something of a collaborative effort, since my knowledge in history is too spread out. I know a lot about history in general, but I don't know much about specific parts of history.
All right. I'll try to be relatively helpful, but please bear in mind that virtually all I've said is some very wild speculation: it doesn't even include a scenario for
how and
when the anti-British coalition in the late 18th century arises, which will be incredibly important in determining the future of this scenario.