Hummm, so let me see if I understand, its kind of like the chicken and the egg. You need drive pressure to get the compressor going, but to get more drive pressure, you need more boost on the inlet side. And since the larger compressor isnt very efficient at low speeds its going to take a little while for things to get going.
With that in mind, you need enough fuel to develop heat which will increase the exhaust gas volume thereby building drive pressure to light things off as soon as you can.
Does that sound even anywhere close?