The MAP fluctuations while on full boost are typical for a wastegate valve that is binding. I would take apart the wastegate and check the valve and valve guide - without the spring the valve should run freely with little friction, ream/hone if necessary to get proper clearance. Imagine that it may bind when the components are hot. Use copper grease and lube it up.
Of course, it could just be a badly working boost control - remove all of that junk and just run with the spring and hose from the intake to the bottom part of the wastegate actuator, that will determine what's causing the fluctuations which probably can't be cured by software.
Boost is building very linear too, that is not how it usually works. Do an intake leak test. Plug the compressor inlet, pressurize the system through the fuel pressure regulator signal hose, and with WOT.
I can see that it is hard to tune the engine with these problems, but at least approach those boost levels with a richer mixture and lean it out, rather than the other way around. A turbo engine can also mis-fire and stumble if run too lean, especially at low speeds.
Set max/min for lambda and lambdatarget to 0.7 and 1.1 to get a better resolution, or use VemsTune log viewer which already does this (open log in other frame).
I would use most recent firmware, which is 1.1.81, it has proven to the best 1.1.x for me. It is very good at revealing if you have trigger errors.