As I recall, you see the beam split and destroy a handful of moons of a gas giant, one of which is presumably Hosnia Prime; a Jovian system, rather than a solar system. Totally works without any need for any arcane inventions by licensed products. You don’t need to resort to that to make the movie work. What’s on screen is perfectly cromulent, and shows a single solar system. It’s right there!
Wait...so your explanation is that Han decided to take the Falcon to visit his old friend, Maz in order to get a new ship so he could throw the First Order off his trail by getting a new ship. Maz's castle is apparently, located in the same solar system as the HQ of the Republic (the Hosnian system), but the Hosnian system isn't a solar system, it's a gas giant and its moons that everyone refers to as the "Hosnian System" even though every mention of a system until now has been about solar systems?
So, let's assume this is correct. Han went to this planet so that he wouldn't lead the First Order to the Resistance base they were heading to on D'Qar. However, your theory is that D'Qar is ALSO located in the same solar system as Hosnian Prime, the capital of the Republic. Wouldn't going to Takodana just lead them directly to the base since they've shown that scanners tend to be able to see everything within about a system before?
Then, when the First Order was bragging about how one shot from the Starkiller could destroy an entire system, they were just joking and it only destroys one gas giant an its moons, leaving both Takodana and D'Qar intact, since they were both in the same system? They didn't even experience debris or anything falling?
Shortly after, they start powering up Starkiller Base to take another shot, but this time at the "hidden Resistance base" on D'Qar. The Resistance has to move into action quickly to blow it up before it fires and kills them all. But why would this have to be a SECOND shot. It blows up system and it apparently fired at the Hosnian system, which D'Qar is in according to your theory.
That makes no sense at all. It seems like I'd have to jump through more hoops to accept that interpretation of the movie than just accepting the the information in Star Wars Battlefront 2, the Visual Guide to The Force Awakens, the official wiki, the official novelization of The Force Awakens, and everything else ever printed about it.
I think it's much simpler to think that Disney wouldn't put out a bunch of false information about their universe and that a movie maker decided to misunderstand physics for a better visual than it is to assume there's a grand conspiracy to cover up all of the planets being in the same system.