Unless you have deliverance cannons (which you don't if you are TEC heh), the only way to colonize a planet in a new system is to camp it out with caps and wait for culture to recede. What can really help here is if you send strike forces(best if carriers, but situation may dictate otherwise) to neighboring grav wells and take out broadcast centers.first thing to do is put up max broadcast centers as soon as you get the planet. a bit later you can maybe scuttle and make room for shipyards/trade etc if you like, but initially you need culture in the new system

There are some research items that help repel culture, etc. so get those as well.
Pretty rough if you are playing hard/unfair, but think of it as a beachhead situation.You'll pretty much roll over the rest of the system if you successfully accomplish this