However, only a fraction of those 13.6 M BTC are available in the market (in the exchanges, or out in wallets of traders who would move them in if the price starts to rise).  The rest is being held by long-term holders who may have rather high "sell thresholds".

I would guess that a convincing "next big bubble" could be pumped up with much less than that.  Perhaps 100 M USD would be enough to buy those "loosely held" bicoins and  lift the price to a point when other opportunistic speculators would rush in and bring further millions.

How much would it take to buy all the coins on the ask books of all exchanges up to (say) 1500 $/BTC? 

(Of course that number would be only a very, very rough estimate, since the asks will be pulled up once the price starts to rise, and on the other hand there will be more bitcoins entering the exchanges.)

Perhaps the June/2014 mini-bubble was an attempt by some whales to do just that -- a pump that was meant to get the "next big bubble" started?