Funny to see this post as I have just converted my triple to a double 2-days ago. Similar set up with Sora STI up front.
I have to adjust the H limit screw. Instead, I screwed down the L limit to lock out the FD from dropping the chain into the now absent granny ring. It took me 5 minutes. Shifts b/t the large and mid chain rings fine.
But at your current situation, it may be worthwhile to start from scratch. Bicycletutor.com has a good video on FD adjustments.

IIRC, to go with compact crankset, you would need to replace the BB as well. C I think the reason is the spindle is a bit longer to accommodate triple chainring. orrect me if I am mistaken here.