Not to digress from the topic too much but
I had a knackered waterpump on a VFR once, the owner was using normal water and some silica antifreeze, i guess this combination had eaten away at the impeller fins (which were all floating aroud the system) the pumps seal had gone and sized at some point, the shaft that connects the pump to the crank had snapped and was sitting in the oil strainer!
Easiest way would be to take the cover off the water pump and visually inspect it, it should be nice and shiny with all of the fins intact... crank the engine a couple of times with the cover off and make sure it is turning ok)
Since the water pump cover removal will drain all the coolant, crack the lower hose off the rad and flush it through with a running hosepipe till the water runs clear, do this from the bottom hose so it comes out the rad cap too (Reverse flush).
Replace the waterpump cover and flush through the engine too.
This should dislodge and remove any crap. You can get a chemical treatment that works wonders too (2 part clenaer / neutraliser from halfords) if there was a lot of rust / crud come out. dont be tempted to use the sand based cleaners, there too abrasive for the motorycle engine.
While your at it inspect the rad, make sure the fins are not covered in mud, when i do this to bikes i often remove the rad and leave it soaking in a bowl of degreaser overnight and rinse it with water aftewards to get all the crap out.. you can get 'fin combs' that will straighten bent fins if you have a lot, as if the air can't flow through it then it wont be working too well.
Last but not least check the thermostat is opening and closing, its easy to remove, boil a pan of water and gently drop it in (dont want to get splashed by boiling water) and you should see the stat open, i think its 8mm at 100c or there abouts. If it doesnt open this could be causing over-heating so replace it.
Connect everything back up and fill with 50/50 antifreeze (try and get a motorcycle / silica free type) and distilled water, this will stop mineral from building up in the block.
Should be good to go!
Back to the op.
The H2 is a lovely bike,
Creamy oil can also be becuase of condensation, I was getting it when the bike was left in the damp and not being used very often, unless your specifically tearing the block to bits I would dump the oil and see how you get on.
For all of the bikes I dont use regularly and havnt put into 'storage mode' I start them up at least once every month or so and warm them up until the fan cuts in and out twice, this will get the oil upto a temperature hot enough to burn off any condensation that has built up.
Hope you get it all sorted out soon, MM will be able to find pretty much anything you need
Word of warning though, if you do look at some of his pics (and I suggest you do!) be prepared to want lots of shiny Titanium, FCR exotica for your new bike
I can attest to the fact that it is all totally worth it though, the bike goes pulls like a train
You'll find plenty pic's of mine on the site cause I am just a pic whore 
But , was the bike started recently and it's just emulsion left from not getting it up too temp' ?
ed this topic a tad! I'll try that thing with rad cap. But if I've blown through into a coolant line surely the pressure would blow water through too, confusing the issue. Your info does reveal that my Gpz does have a duff thermostat though - fire it up cold with pressure cap off and you get a face full of water! And you can get rad combs? Excited! Need one for a spare mini rad I've got!