Have you investigated the possiblity of one of the BOV's leaking?
Split hose that only opens up on boost?
I would imagine a "stuck" or seized turbo would effect the running of the engine at all conditions not just when coming on boost. It would be like restricting the exhaust massively on the rear 3 cyls at all RPM'S, not good
If the car runs fine off boost at all revs, to me, this would point to an air (boost) leak. Black smoke = unburnt fuel.
Remove the AFM's and blank off holes, pressurise inlet system with compressed air to 15psi and use Snoop or Fairy Liquid/water mix in a sprayer and spray it all over the inlet and turbo pipework, check for leaks that way.
Just my thoughts
Are the turbo's ceramics?
Hope this helps