Just google "evga 600b psu tomshardware" and you will get to know what I am talking about. Not to mention the reasons I have given you multiple times for the same along with the Tier List. There is no point going for a a higher cpu/gpu with a cheap psu when you have the risk/possibility that it can blow out both. I am sure if you ask any of the moderators over here, they will validate the same.
About cpu cooler, OP has already mentioned that he is goinf to OC the chip. The cooler you have linked is at best good enough for stock cpu clock. For overclocoking either a 6700k or a 75600k its not going to hold the temps. There is no point repeating "it will do the job" when you know that it doesnt stand a chance on competetive clcoks for reliable units like Noctua or Deepcool. Even Cryorig units are better at relatively cheaper price than the one you have listed.
BF1, Farcry, watchdogs, none of them uses more than 4 cores optimally. I never said 4 threads, donno where you are getting to that from. And i really dont understand why you are after 6700k when i never said that its a bad choice.
As for the alternative, I have already provided the build most suitable for the price range, with all decent quality parts and nothing cheaped out to accomodate something else.
Anyways, i think enough has been said and this is not helping the OP anymore. OP has got all the information he needs and will be able to make an informed decision.