After 6 (?) jumps from your homeworld, the max allegiance (without culture) is only 25%. Culture adds 10% (or, if you have the tech for it with Advent, 20%), but if you actually want the allegiance bonus you should consider moving your homeworld to a more central planet. (you'll still need to use culture to raise the allegiance throughout your empire, but the maximum will be much higher, hopefully).

Deliverance engines shoot "culture" at other planets, it makes the culture spread really really fast, but you can never exceed your maximum allegiance on a planet, for advent 45% with research and the others 35%... on really big maps, that extra 10% does mean that you do get quite e bit more resources than the others. but the map has to be fairly big for it to be significant...

You could move your capital planet to a different spot to make it have more planets closer to it, but other that that, there's nothing you an do...

Oh, and on a side note, it's fun to have 10+ deliverance engines of auto fire in a multi star game, it's hilarious to have your culture cover half another solar system. and it'll really screw with their planet tax income and resource collection and force them to keep rebuilding planets if you do eventually cause a revolt.