The next to last pic (labeled "PWM fluctuations?") does indeed look like a classic PWM signal. I don't think it is the VCore signal though. The frequency of the signal in the pic is about 18Khz. That's more in the range of the main P/S switching frequency and well below the bottom end of the HIP6051's spec'd operating range (50Khz to 1Mhz). So, it's most likely from your main P/S. The other
possibility is it's from the video circuit (vertical sync) and the decay is caused by the capacitance of your measurement methods (the twisted pair wires). To figure out which it is, you could look at your +5V and +12V rails coming in to the m/b and while looking at the VCore switch your video mode and see if the frequency of the signal changed.
In general, from looking at those pics the basic answer is -
1) a VCore circuit that has poor dynamic load characteristics do to a) single-phase design b) too low a frequency of operation c) poor frequency response on the output filter d) all 3 of the previous.
and
2) poor power filtering do to a) not enough bulk capacitance b) too high ESR values on the bulk capacitance c) not enough or incorrect values of high frequency decoupling d) too much inductance inline with the filter caps e) all 4 of the previous.
If you remember, there were a lot of issues with VCore supplies when the P3s first came out and m/b manufacturers scrambled to adjust to the high dynamic current requirement presented by newer processors. The situation became tougher when AMD released their newer processors, which were even more demanding. These things are why now you see 3-phase (and even a few 4-phase) designs, extremely low ESR bulk capacitors, much higher (up to 2Mhz) operating frequencies, and newer PWM controllers that adjust mid-cycle (newer ASUS boards) for VCore circuits.
Regarding the HIP6021, it is spec'd as having a +/-6.5% dynamic load tolerance. At 2.05V, that's ~133mV (which is in line with your observed measurements).
As far as your Vcore adjustment circuit - you won't be able to affect any improvement regarding the types of fluctuations you show (short term, lasting in the usec range). To solve those with the existing VCore circuit design, you only have 2 feasible choices that I see.
Depending upon the HIP's current operating frequency and the inductor used, you could increase the operating frequency to help with fluctuations. It won't solve the problem, just help some. There should be a resistor connected to pin 23, this sets the frequency. The limiting factors will be the inductors used in the Vcore circuit and the gate capacitance of the MOSFETs.
The other route is to improve the filtering. Don't know what's on the CUSL in that regard (ASUS usually is pretty good in this area), but the goal is to increase the total bulk capacitance (there is a limit do to surge current issues), lower the impedance of the filter and power distribution (lower ESR on capacitors, lower inductance in the circuit connections), and improve the high frequency filtering in the range most needed. To do this, you would need to look up the specs on the caps currently used to see if lower ESR caps are available (and higher capacitance in the same footprint). Sanyo, Rubycon, and Vishay all make very good ones in that order. (don't like the nichicon ones much myself) To lower the inductance in the circuit connections, you can use braid or multi-stranded silver wire to parallel m/b connections. Ground connections are of particular importance. For the high frequency filter side of things, adding high quality ceramic caps of either .1uf or .01uf at strategic locations would help. (across the bulk capacitors, stacked on the processor socket pins/existing capacitors). So would lowering the inductance of the circuit connections.
Of course, the question becomes - how much effort and expense for what gain - is it worth it
ps. You might want to turn your signature off when posting a sequence of pics like that out of courtesy to the great guys that provide these forums
Of course, my blabbering sometimes should probably be limited too :O