i think that if a planet had so much gravity, that all the planets and sun(s) in the system go around it, the planet in the center could be populated with glitches, because of the fact this is what people believed back then, but it is possible if the planet has Too much gravity, entering it could crush you upon arrival in the atmosphere.
That would be interesting. Not sure what gameplay elements it would bring other than insane gravity. It would also be physically impossible naturally, so there'd have to be some sort of explanation. Perhaps a super advanced yet very religious race does this to their homeworld using massive gravity modification fields, to set the universe right.
This would still cause massive problems; any planets the same distance from you as the star would be wiped out; other planets would become so hot they'd become manga planets; further further out planets would be inside the "habitable" zone for amounts of time relative to how long they stay near the star per each cycle; the furthest out stars would basically stay the same baron ice planets, but the planets that used to be closer tot he sun (and therefore hotter) than you have a chance of becoming iced over. This is all dependant upon whether or not there was more than just their planet in the solar system. But still, I think it's quite cool. They, similar to us in our early years, believed God made us and then the heavens around us, therefore leading to the conceptualisation of us being the centre of everything. They had a similar thing, but they were so die hard and unified in willing their God to be right, that they corrected their solar system to fit their God's plans. Could be something weird sounding and completely fake like a "quantum weight virtualisation unit" or something that, instead of increasing gravity to uninhabitable amounts, could instead twist the fabric of space around their solar system, causing matter to effectively be "tricked" into thinking that their planet had the most mass, not the star- but that would eradicate your idea of a hyper-gravity planet.
I suppose you could fake it by having a solar system with one planet that has a whole bunch of moons. From the perspective of the people on that planet it would be hard if the system was geo- or helio-centric. Alternatively, you could have a black hole that was surrounded by a habitable shell, and have multiple stars orbit that. Technically it's not a planet, but outside of holes that go down to the hole itself, you have no way of knowing. If far out enough, the surface should have a manageable magnitude of gravity.