There's also a ton of misdirection spells/items available. You could try to give them a different dragon every time they scry using the blood.
True Seeing does not see through mundane disguises. While I hate to consider what such a thing might look like, a dragon with ranks in Disguise and a quality disguise kit might be able to fool the PCs into thinking it was a different dragon, or a different kind of dragon altogether. If the dragon knows it's being scryed upon, it might take certain steps to confound the diviner. If it's instead a Master of Many Forms, it has disguise as a class skill. If Clark Kent can separate himself from Superman with a pair of horn rimmed glasses, surely a Big Bad can do something more impressive. If the PCs see a Blue Dragon the first time, and a Silver Dragon the second, and a Copper Dragon the third, they might think that either the dragon blood on the cloak is a diversion, or that their crystal ball is faulty.
As far as scrying "ruining" your game, I like the previous suggestion of a "Trousers of Time" style divination, put forth here:
well you could do the multiple streams of the future that can change if such and such thing happens like your characters ignore a village asking for help or something like that it can change the future
So if they try to see the future, they see only one possible future, and can take steps to make it come to pass or to change it. Or, they see one part of the larger picture. Take an opportune moment out of context. If all they can see in connection to the Big Bad is an NPC screaming "You'll never get away with this!" -- well, how useful is that? If all else fails, just have the Big Bad run the show from a distance while on a tropical beach.
IMHO, the whole construct thread is much more complicated and irritating than simply making the dragon a lackey or partner. Granted, a dragon-shaped flying machine with hydraulic breath weapon and ritual-based magic all bundled up inside would be a kickass and truly scary thing, but what if the big bad were simply riding the dragon?
Just thoughts. Take what you want.
-Red