I'm of the opinion that Stride likely was familiar with and chose the spot and that it offered sufficient darkness/privacy to allow her to be paid for services rendered. I don't feel as if the shortcomings of Dutfield's Yard caused the killer to abandon his attempts at mutilation. Deimshutz's arrival likely did that.
If she did as you suggest, she was not very discreet, as the murder spot was almost on the main street, whereas further down yard would have afforded much more privacy.
As to why there wasn't any blood in the mouth, there's no reason why there would be - unless she was up side down at some point. Blood goes where it is pumped, or where gravity pulls it. There's no reason why punctured lungs would cause blood in the mouth, when the punctures in the lung is precisely where the blood would escape. When people cough blood, it's because the lungs are bleeding internally (usually from infection), and the blood only has the one way to go. If the blood has anywhere else to go (say, through multiple stab wounds), it would take some time before coughing would bring blood to the mouth - more time than Martha would have had.