Since you already think "chords", that's a big part of the battle. Playing those as single note lines, combined with major, minor, chromatic, etc, etc will get you started. Modes are the next step, to truly "paint" interesting and relevant stuff you might not otherwise think of.
Both of the things you've said are valid (to me). I come from fretting *very* hard on acoustic. I need to learn a lighter touch on electric. I often do go sharp. I've already looked at lessons like justinguitar, yousician, guitar tricks - and need to check out the solo app mentioned above too. One of the more frustrating things is what you said - I already think in chords and am fine with runs/hammer ons/pull offs/any advanced acoustic finger style. Just need to find a place that will let me run with scales/lead practice. Thanks everyone for all the responses.