I’ve come to accept the Starkiller weapon, since without it the movie would definitely lose tension in the third act. However, that doesn’t mean it couldn’t be better introduced.
This is a variation on Restructured:
There is a defensive installation on a moon of Takodana or an autonomous defensive station, which is taken out by Starkiller so that Kylo can attack the castle. If it’s a station it could be generating a planetary shield. This allows for the inclusion of shots like Kylo watching from the bridge of the Star Destroyer and some of the original effects of the distant Hosnian wreckage. You could also keep lines such as ‘It’s the First Order, they’ve done it!’ and ‘Finn’s familiar with the weapon that destroyed the (defensive) system, he worked on the base.’
This concept would require some effects work to establish the satellite/moon. I think it would be effective to use the wide shot of the Hosnian system except with just a single beam of energy hitting one of the more remote planets turned satellite with Takodana in the foreground. I think an autonomous defense station would make the most sense here, so that it could be established in the shot where the Falcon arrives at the planet, heavily armed with its weapons trained on the Falcon. It could also be in stable orbit over the castle.
This would effectively establish Starkiller Base and its range and accuracy using a Rogue One style ‘single reactor’ attack. It would be dramatic enough to substantially raise the stakes, but still modest enough when used on this remote pirate base to justify the Republic’s continued inaction.