Is there anyway to prolong Hanoverian resistance?
Prolong Austrian and Saxon resistance and you'll prolong Hanoverian resistance. Support, even diplomatic, from France would help too.
Of course, that raises other problems.
There's a truism taught to students in law school: Never ask a question in court which you do not already know the answer to. Bismarck operated his foreign policy along similar lines. He never began a war which he wasn't already extremely certain Prussia would win. Not 100% certain, obviously, but north of 80% definitely.
Bismarck would carefully set the diplomatic stage, isolating his target, roping in allies, and taking other measures. Bismarck also understood what Prussia's precise capabilities were. Roon and Moltke the Elder never lied, for example, to Bismarck in the manner Moltke the Younger et. al. lied to Wilhelm II and Bethmann-Hollweg.
As we've discussed in a few recent Franco-Prussian War threads, a tougher/better prepared France is something Bismarck would be aware of, acknowledge, and accommodate in his plans. Similarly, a tougher/better prepared Austria, Saxony, and/or Hanover are also something Bismarck would be aware of, acknowledge, and accommodate in his plans.
Thus, just as tougher/better prepared France would mean a very different Franco-Prussian war or no war at all, tougher/better prepared Austria, Saxony, and/or Hanover would mean a very different Austro-Prussian War or no war at all.
Can Hanover attack the Prussian Rhineland?
I don't think so. While in the OTL war, the Saxon Army immediately and deliberately abandoned Saxony in order link up with Austrian forces in Bohemia. The Saxons did that, however, because they knew they could not really defend Saxony while joining forces with Austria in Bohemia could help win the war when the main armies clashed.
The Hanoverian Army could possibly do the same, abandon Hanover to seize the Rhineland, but that wouldn't be seen as immediate a war-winning measure as beating the main Prussian armies in Bohemia would be.
It's the mid-19th Century remember. In the European viewpoint, wars between the great powers last a few months or a year at most with the main armies clashing quickly to decide matters. Seizing an enemy's industrial heartland to cripple their ability to make fight a long war just wasn't planned on. Britain always planned on blockades, but the continental powers always planned on things being wrapped quickly and did so right up through 1914.
Ultimately I am wondering if the war with Hanover can be prolonged (in Hanover or the Rhineland) for a sympathetic France to get involved usefully - deploy some troops to the border with Prussia?
As I pointed out earlier, if France isn't neutralized in some manner, and Bismarck took great pains to do so, then the war isn't going to happen.