So, Steph is my favourite DC character and I really had to comment on this idea (it's actually why I registered), as I really hope you follow through on it.
One thing you could do that simplifies her having Amazon blood is have her descended from the Bana Mighdall Amazons who lived in Egypt. They've since moved to Themyscira so you could still have Steph go there for training. They are also the more aggressive Amazon tribe, so she might pick up some fun attitudes during her time there about the place of men and relationships. There is also at least one canon half-Bana in the old DCU with super-strength - Grace Choi. As far as it being triggered, maybe her mother has a family heirloom that, when Steph touches it, kickstarts her Amazon blood?
It would be particularly fun to see her show Tim her new moves given how he tended to underestimate her at every turn, particularly if he's being distracted at the same time. He always came across as pretty clueless so having Steph turn him on and wrap him around her little finger would be very entertaining. Between Steph's pretty impressive curves and such, he'd have no chance at all.
My stance on the height/build thing... I think I'd go with her staying mostly as she is, so that it isn't immediately obvious *how* strong she is. Also DC Amazons have supernatural strength so while she would be in a lot better shape and well built after a stay on Themyscira, she wouldn't be likely to be a bodybuilder type. I think Barbara is meant to be around 5'7" tall though? So you could have Steph hit 5'11" or so which would actually make her an inch taller than Nightwing's official height and considerably taller than Tim. She'd still be shorter than Bruce but she'd still be taller than the rest of the Bats.
Hopefully, some of the above might be useful and I'll be watching this thread - like I said, I like this idea and hope to see it written. If there's anything else I can usefully comment on, please say as much.