Yup custom race is the ticket! GO SQUIRELS GOOOOO!!!!!!
Ahem... My race includes a 30% economy bonus and a 30% influence bonus. I also use the pacifists for a party as they have another 20% influence. Then I grab up all the influence wonders as I go. and any resources I see. I will often buy them if I can't get to them first. I will often flip planets with out even building a starbase.
As for seeing how much influence is being pressed on a certin planet you must first do espoinage on that race. When you hit LOW level you can click on the planet you are intrested in and you will see the amount of influnce that it is producing and then in parentheses beside it you will see the amount of pressure it is feeling from other cultures. When that number reaches 4 or higher it will start rolling each turn to see if it flips.
As for actually making them flip influence is a combination of military might, population and resources. So build (or at least appear to build, GG spin control center) a military, get lots of people and make sure and snag those influence resounces.
Also when trying to flip planets start with the lower class planets on the outskirts of a cluster. If you try and start taking a 5 planet cluster where 4 of them are PQ 10+ then you are going to need 5 or more stations. Start at the outskirts and it will be much easier. As they flip they will help you with the next planet and they will domino.
Felk the Suave