Took some debating but had to convince our local lodge this build would work however there was much questioning as so how you get Improved Unarmed with this building as the Archetype for Strangler at L1 replaces it.
"At 1st level, a strangler deals +1d6 sneak attack damage whenever she succeeds at a grapple check to damage or pin an opponent. The strangler is always considered flanking her target for the purpose of using this ability. This damage increases by +1d6 at 2nd, 8th and 15th levels.
This ability replaces unarmed strike and brawler’s flurry."
So I assume you're taking IUS for pre-req on feats later on? Otherwise why not just take it with Tetori as first level, getting IUS and Improved Grapple from the Archetype without having to blow a feat right out the gate? So with Tetori you'd get IUS and Improved Grapple from the archetype, you'd lose the 1d6 starting from strangler but save 2 feats at the cost of delaying the building one level. Assuming that's not an issue, then beelining for Turtle Clutch would give it to you by L2 but you'd be doing 1d6+4+1d6. Unless it states it somewhere (from what I was told) then you'd get to keep the IUS from Tetori but not from Strangler so the d3 would be a d6.
Also it should be mention that Martial Flex or any of the freed up feats can go towards Accomplished Sneak Attacker for another 1d6. And while I'm not going to count it on here, I could have sworn there was an ability somewhere that moves the d6 up to d8 as well. I'd assume most of the time there's be a stack of notes cards with feats to rifle through as you need them.
Other feats to consider: Knockout Artist, Surprise Maneuver, Sneaking Precision, and a whole list of teamwork feats. I second the notion on using Sap feats as well.
Now I might have gotten carried away without all this but I'm not one to build a character without a plan and there's a few variation of a "best grappler" build out there. With the entire to play society games and they're dreadful happy of always wanting people alive, I thought the idea of making a Cajun style gator wrestler was pretty hilarious. Considering he doesn't even really speak Common and just mumbles most of the time before launching into combat and putting sleeper holds on anyone or anything. Plus it was Irwin's birthday yesterday and it's only right to do something stupid along those lines.
Edit: Mathfinder is confusing as s*#%. So, you get IUS from Brawler anyways. (that helps the understanding a bit) but you lose Unarmed Strike from the archetype. If you were to then blow a feat (since I don't see where you've added in the feat every odd level anywhere) for Unarmed Strike, would you then have it anyways? Saving Martial Flex for any situational feats and still having feats to blow on other things as they present issues. Otherwise the mentioning of Tetori is very odd for an almost solid Strangler build throughout. I'm just wanting some clarification as it's a good build and sounds like a fun character but my brain needs details.