I trade at this size every day, on multiple venues, and can share these observations:
1) IB's arbitrary limit on the order size in unimportant. Regardless of the size of your order, you will receive partial fills in the 1-2 million range, so it really doesn't matter how big an individual order is. This is true for EBS and Reuters also.
2) You cannot expect to fill this size in under 5 seconds, in a normal market. You are correct that LP's will back off their quotes after they get hit for some amount. If you stick around with your limit order it will often get filled eventually, of course.
3) It is possible to go elsewhere and get quotes for a minimum size, such as 10 million or larger. You will pay a couple of pips on each order for this -- for me that is too much to pay. YMMV.
4) Moving to EBS or Reuters only helps for a few currency pairs. For the rest of the crosses, you are much better off at IB. Currenex is not as good as any of the above usually, but there may be local variations depending on your broker and the time of day which turn out to be pretty good.
5) No matter where you get filled, it will affect the offering prices at all other venues immediately. A few years ago that might not have been true, but the LP's improved their technology.