No offense taken. I did not feel personally insulted at all, but you probably know that some AH writers project the opinions of 1914-1945 about Germany back into earlier times. Which leads to sloppy AH.
Anyway, you make a lot of good points.
Hanover is in itself indefensible against Prussia unless you station a lot of additional troops there, which no one will want to pay for.
Either Hanover allies with Prussia as a junior partner, protected against treachery by the idea that the wrath of His Britannic Majesty is not to be taken lightly.
This, of course, either means that Hanover will stay outside of the Prussian-led Closer Union and in an alliance with that Germany in a position similar to A-H. Or it keeps this TL's United Germany much looser than the OTL 1867/71 version. In fact, it might be based on the Zollverein as an EEC parallel.
Or Hanover follows a rather antagonistic course towards Prussia. As always since the early 18th century, that means the King needs a strong ally that will be able to hurt Prussia enough, so Hanover will be restored during the peace talks.
a) France? For a German king to openly ally with the Orleans kingdom against fellow German monarchs is a PR nightmare. George will have every German publicist to the left of Tsar Nicholas aginst him. Loudly. The memories of the Liberation Wars against Napoleon are far too fresh.
b) Russia? The same as above, only moreso. Russia was only favored by the fans of absolutist monarchies. While the majority of the German Nationals were Liberals and rather against "Kings' Rights" that kept particularism strong
c) Austria? Possible. The Emperor wil be seen as a power that can at least balance the power oif Prussia, but Austria still is rather far from Hanover and cannot easily project force there. The best of the three not-really-good options.
Reagrding investments: Must the UK government sent money there instead of elsewhere? Favourable condition for private investors from Britain might already help.
I'm examining the antagonistic version, as that is the one that has the largest difficulties and the one that would most likely occur (as I don't see Prussia not wanting to have Hanover join in the German Empire as a constituent kingdom, at the very least). As such, looking at OTL, we see Austria actually allying with Hanover and many of the larger German states and losing in 1866. In that war, they were surrounded by hostile states and eventually were overwhelmed by superior numbers.
If we have Great Britain still in a personal union with Hanover, they may not take part in the war at all, but it is just as likely that, considering that (all things being equal) they would be surrounded by the new North German Confederation. You might see the citizens eventually desiring a union; if the King of Hanover doesn't allow it, the nationalists may try to enact unification themselves.
In order to avert this, the Austro-Prussian War must be averted (doubtful) or end with Austrian victory (moreso). It might be interesting to see a British-Austrian alliance in the middle of the 19th century. This could be enough international support that German Unification doesn't take place, or that it doesn't include Hanover in addition to the South German states (and maybe Saxony). Of course, this also means that the future Germany, as it were, would be a snake of territory between the two sides, which I don't see as really tenable.
In the end, for an independent Hanover, I would say a few things are important: have Oldenburg, Brunswick, Hamburg, and Bremen (along with perhaps Saxe-Lauenburg & Lübeck) to be friendly with Hanover. This means that their nearby borders are secure and they have some common unity in the region. Perhaps playing up the Low Saxon heritage and differentiating from High Germans in South Germany and the Prussians in the East might help, but that probably wouldn't do anything until the 20th century.
Another thing that might draw Britain and Austria together might be a long term common enemy. Perhaps have the Ottoman Empire start to collapse in the 1830s/1840s, with the British needing someone to fill in the gap to prevent the Russians from moving in. The Austrians could, possibly, get carte blanche to move in and prop up the European side of the straits. Not that this would likely do good things for the Empire's long term survival.
At what time can the P.O.D. take place? Back in 1714? I've been assuming P.O.D.s from after the Treaty of Versailles, but we could go back to 1700ish in all reality and still have the personal union come into effect.