Qt: Convert to strongly-typed connects

@chub Several months ago you asked me to make use of Qt5-style strongly typed connects in some Qt-related MR; I promised to get it done in a follow-up. I actually decided to tackle this for the whole plugin in one go, and I've finally now gotten around to completing that work.

This covers 99% of cases using the old style. There are a few cases (8) remaining unfixed due to some complications.