K03 turbo swap to k04 with a tfsi ea113

Hi guys I have finished a a full engine rebuild and been enjoying the car but now want to give the old girl some more punch with more boost. I looked up the spec for a k03 and 0.6 bar 8 psi is the max flow. So remap doesn't seem worth doing just yet as I I have a new hpfp new belts and a full rebuilt head and an uprated diverter valve. So putting a new turbo on seems ok and I have the standard injectors so remap then allows the for the turbo being able to boost without being strained.

I no there are kits but looking at them I have most of the parts apart from the injectors everything else I have fitted or the car already has like the intercooler precat removal. If anyone can help that would be great