Why did Eurostar order Velaro's from Siemens instead of the AGV from Alstom?
Cost, Siemens offered them a better deal.
Additionally Alstom wasn't & couldn't offer the AVG to Eurostar, it didn't meet the specs. Whatever Alstom would have provided would be a new build (using existing technology;) pretty much the same thing they are planning on doing for the Acela 2 (if they get the bid.) Alstom did sue multiple times to get the bid from Siemens, but eventually lost all their lawsuits, and decided to end litigation.
Trains traversing the Chunnel have/had* very strict rules one construction, flammability, rescue capabilities, etc. Which means you can't just take an existing train, repaint it and run it thru the tunnel. The new Class 374/e320 is a fairly heavily modified Velaro to fit these new specs.
*Some of these rules have been lessened, but I don't recall what exactly; Google will know if you're really that interested.
This all being said, I don't really understand where you are going with this line of thought with the double-deckers. High Speed 1 (the British line) isn't near capacity, they can still fit more trains on the tracks. So inventing new double-decker high speed trains to run on HS1 isn't really viable in any sense of the imagination.
Why are we trying to fix something that isn't broken?