Running a BS3, i wouldn't be looking at any of the names mentioned here. Id be asking around on yellowbullet for someone who knows their shit, and consider trailering it out of state if necessary. Im assuming you're talking about a car set up to race, making in excess of 1000hp at the crank. Id have one hell of a time letting joe schmoe at any speed shop tune something up like that, when 90% of his experience is cookie cutter LSX builds.
As a person who has done EFI custom tuning on GM and Ford cars for the last 7 years, I disagree with the portion of your statement alluding to the point that those who tune street cars are somehow less equipped to handle the tuning of pure race cars. As any other experienced EFI tuner would likely agree with, tuning for WOT is easy when compared to tuning for driveability. So, since racecars don't necessarily need as much dialing in within the driveability department, whereas street cars do, usually street cars are more of a challenge to tune; assuming it isn't all just cookie-cutter tuning. However, even in the cookie-cutter tuning, you still have to nail part-throttle driving down due to minute nuances between cars equipped with similar/same hard parts. Also, it has become pretty common for Joe Schmo shops and local backyard tuners to tune 4 digit crank hp cars these days, so there is nothing that discriminative about that power level anymore. Sure, 10 years ago 1k+ hp was a holy grail, but now it is just another check in the box on the way to bigger numbers and faster ET's. I am not suggesting that just any local tuner will do, but the idea that to somehow get better quality of workmanship one must travel, is absurd.
If this were my car, and I were looking for someone else to tune it for the 1320, I would be searching for someone with experience with the powertrain itself, as Izzy already mentioned, and also the management system too, whether that be FAST, BS3, Megasquirt, etc. If a local shop can cover that task with solid results then all the better when it comes to any future retuning needed. A phone or face to face discussion with the tuners for the shops mentioned previously will be able to weed out any that the OP feels unfitted for the job.
Best of luck with the search Izzy!