No.. insufficient wastegate spring pressure will cause you not to be able to hit target boost, not at all what you're describing.
What do you mean you're thinking about getting an internal wastegate for a 20g? Do you mean the 20g you are planning on buying doesn't already come with an internally gated turbine housing? AFIK all aftermarket stock location turbos come with internally gated turbine housings.
Also, the HKS SSQV BOV you're getting is known to leak, it's going to give you problems. The stock BPV will function much better than that HKS unit.
For what it's worth, the symptoms you are describing sound like boost cut to me. That would be something to talk to your tuner about.. often times they don't really tune for 5th gear, which will see higher loads, and in turn higher boost than the car is actually tuned for. I'm assuming you're not getting any CEL when the car bucks?