The royalty idea would need work, and somehow be referenced elsewhere in the film, but I think it provides a novel way to solve a lot of problems at once, some of which I’ve talked about.
The concept of the New Republic being infiltrated by First Order sympathizers has the benefit of EU support, but the Skywalker lineage and in particular the idea of a Skywalker being the heir to the Empire also has this support (One of the EU books is called Bloodlines for a reason). But the biggest reason I don’t like the sympathizers angle is that it makes the Republic a lost cause before the movie begins. How much sympathy can we give a government that is already halfway towards tyranny? Also, it seems rather silly for the First Order to blow up the entire Hosnian System if they were effectively turning the Republic from the inside. Surely they would have lost a lot of their own supporters in the destruction.
As for Luke’s reason for going into exile, I see one explicit reason in TFA ‘He just walked away from it all’, and a continuation of this reason in TLJ ‘It’s time for the Jedi to end/I came to this island to die’.
These don’t feel very compelling for a character who is motivated by optimism. I think it would be much more compelling to give him a constructive reason for going into hiding, and that could have to do with the attitude of the galaxy to the Empire and its line of succession. Granted that little is known of galactic sentiment or politics of this era from the movies (there’s almost nothing about this in the sequels so far save from a line from Snoke calling Kylo ‘heir apparent to Lord Vader’) but this makes it that much more fertile ground for development. I imagine that there could have been several splinter organizations after the fall of the Empire, each attempting to claim ownership. An heir to the Imperial throne would legitimize their claim, and rally many systems to their cause. Remember that it was the death of the Emperor more than anything else that led to the fall of the Empire as it was seen in ROTJ, so the problem for the Empire is not one of ships or soldiers so much as legitimate leadership. The First Order has a leader which has many of the powers of Palpatine, but these abilities didn’t convince everyday citizens and senators to support him during his rise to power - most people were unaware that he was an evil space wizard until too late. It was the legitimacy bestowed by the Old Republic system of government which allowed his rise to power, and so imagining an analogue for the Empire and its succession seems natural.
This brings us back to Luke Skywalker and his importance. I never understood why the First Order was so intent on killing a single Jedi who had already run away and clearly wasn’t a threat. Sure it’s a priority, but the top priority? And why does everyone in the Republic assume that a single Jedi can stop the First Order when ten thousand Jedi weren’t enough to save the Old Republic from a couple of Sith? It cries out for a reason, beyond him being a Jedi or even a legend.