Now, I know this is connected to something I really shouldn't be doing, but anyway, bear with me here.....
I have, once, managed to fly EGQL - EGYP with the C1K - with literally vapour on touchdown... anyway, I've been trying to replicate this with better flying (for me)

I've extended the range (allbeit with illegal reserves) of several of my 'favoured' A/C with decent results (EG even with real weather I can, for instance reach a given airport with fuel within 2-3% each time)...
Now, to the C1K.... I have had this machine up at FL500 several times over the UK (As part of my long range calculations) and it flies very well, with no tendency to drop or stall. This is an upper limit, but FL450 is 'well' capable. I have just repeated this before typing.
Now, to the Falklands flight. I make an immediate turn onto 200-ish degrees (Course is 222 from EGQL) and commence a maximum climb (290Kts). The A/C gets up to FL350-70 without issue, and I then use time compression. After each 10% of fuel is burned off, I drop to normal speed and initiate a climb until I lose three or four knots off the cruising speed. I then let more fuel burn off and repeat the cycle (the aim being to maintain speed and increase height). I always use normal speed for this for obvious reasons. Now here's the query (at last I hear you all say)...
Above FL415, I keep getting what looks like a 'Dutch Roll' - but the A/C doesn't swing it's tail out, it's just the wings which wag up and down. No matter how light it is, I cannot avoid this - now, I am usually within about 2000 miles of the Falklands when I'm ready to go to this height, but always need to drop to FL390, then coax her back up to FL400/405. **But**, If, for instance I take off from Leuchars and head in any direction, I can extablish FL500 with no issues (except time to get there).
Anyone have a clue why this is?
Incidentally, currently, at around 1800 and 900 miles out (from the Falklands) in real weather I have achieved positive fuel remaining (IE DMs flight computer gives me either equal or up to 100 miles positive range compared to distance out) - although this gets radically altered if (when) the wind changes - but I am working on further refinement of the cruise climb to steal even more range.
On the last attempt, I was forced to rendesvouz with an (invisible) tanker from EGYP at 500 miles out, as fuel had got to the 'no chance' range..... :o
So, ignoring the daft bits, why do the A/C behave differently at altitide depending where you are? (My uneducated reasoning is that at altitude the weather is faiyly uniform?)