Since the idea of the base charging their weapon is the ‘ticking clock’ for the final act of TFA, I don’t think the weapon can be eliminated without negatively impacting the film. So with this in mind, and considering the idea of having the Star Destroyers attack the Hosnian system, the only way I can see it working is that the Starkiller is targeting the Resistance base like in the original cut.

I imagine the sequence of events to be as follows:
Snoke’s first scene is moved to after Maz’s castle, and Hux advocates a strike on the Republic. Snoke sends him to oversee preparations for the Star Destroyer incursion.
After the Han/Leia talk, Rey is interrogated by Ren and she sees his vision of the weapon in operation.
Directly after this, Hux makes his speech, leaving out the part about the ‘fierce machine’ bringing an end to the Republic and the fleet. Intercut with this are snippets of the Mega Destroyer incursion and the destruction of the capitol city, with a desperate defense by the republic bombers and the sacrifice of Rose’s sister.