I agree 100% with Jay... too many people are led to believe that a bigger turbo will act exactly like a smaller turbo. This is not true!!! Off the line can be helped but like Jay said, locked in OD at lower rpms it will be easier to notice the difference. Do the test from around 2200rpms and I bet the turbo will light off like a rocket. Then do the test at like 1600 rpms and I bet it will feel like a laggy turd.
Tuning can help. Have the tuner make sure it does not lock the tc into OD so easy and so low.
Gears will also help. Raise that RPM level more
Smaller tires will help. This raises the rpms and takes a little load off the motor
Air flow mods will help like a ported intake, aftermarket air filter, up pipes, manifolds, etc... They will actually improve the volumetric efficiency which will cause the turbo to operate more efficiently at lower rpms.
Much of this has to do with the efficiency area of the compressor maps (different turbos operate differently at different area of the comp map)... It is something easier explained over the phone... but I will try here.
I am not sure if you understand all the different terminologies but for this discussion I would focus on pressure ratio, Air flow, and the efficiency islands. A simpler way to think at it is pressure ratio = boost, air low = rpms, and efficiency islands = temps (those are not exactly what they mean but it helps to understand better).
The higher the pressure ratio the higher the boost
The higher the flow the higher the rpms
the higher the efficiency the lower the temps and the better the turbo will run and spool up
here is a general map. You can see that the closer to center of the map you get the more efficient it is. This also equates to lower temps. The farther you get from the center, the higher your air temps get, which raises your egts. Also the quicker you get on the map and get to the efficient areas of the turbo, the quicker the turbo will spool up and make efficient power.
Here is a map comparing the pmax to the stock turbo. The green area is where we spend most of our cursing time (around 1600-1800rpms). You can see that it is very close to the center of the efficiency islands of the stock turbo and that it is way out of efficiency of the larger pmax turbo. Which means that at the same psi, same boost, same rpms... the stock turbo will be putting out cooler air. Also you can see that the smaller turbo can put out more boost at a lower rpms without surging (that would be the top left areas of the compressor maps) I know this is not your exact situation but it illustrates the same points as to what we are talking about. Smaller turbos operate better at lower rpms and lower boost.
The green area = 1600-1900 rpms
the red area = 1800 - 2100 rpms
Here is another picture of where we spend most of our time at 3/4 pedal - WOT on a spirited run. You can see that now you are almost dead center on the efficiency island of the pmax and now the stock turbo is way out of its efficiency range. This is one of the reasons why a bigger turbo like the pmax will will feel so much faster on the high end, spool faster above 2200rpms, and lower your WOT egts,.
There is a lot more that goes into it than just this... but it should give you and idea of what I am talking about. You will also note that I did not plot just one little tiny point on the maps... that is because our boost and rpms fluctuate so much with tire size, speed, tunes, volumetric efficiency, etc... so some people might experience slightly different results but the general principles are the same.
bigger turbos generally takes longer to spool/light
Smaller turbos operate better at lower rpms
bigger turbos generally equals higher cruising temps
bigger injectors generally equals higher cruising temps
bigger tires generally equals higher cruising temps and spool later
higher elevation generally equals higher cruising temps
Now before anyone nit picks my calculations.... I did not really make any. I just guestimated to show general theory and not exact plotting points. Also I know every map is different but these ones were easy to find and illustrate the principles were are talking about