@nilsbert.
When I was at about your speed I did almost the same thing as you. If you keep practicing slow solves, you will get better averages but not as good singles, which you probably already knew. If I were you I would do mostly number 3, it will help your lookahead as well as your TPS. You should also try to do number one a lot as it is the fastest and best way to improve lookahead. I would stay away from number 2, since you won't get hardly any good lookahead practice at all.
Also, make sure you have a good cross and that your cross to first f2l transition is smooth. This is what I find the hardest to consistently do, but when I do I get great times.
As for your LL, the same thing happens to me. What I usually do is turn fairly slow (good lookahead speed) during the first three f2l pairs, and then speed up during the last pair, and then turn almost full speed for the OLL and of course the PLL. However, everybody is a little different, so you might have to do things a little different. If you dot know the best speeds for different steps, do a few really slow solves. The steps where you have the best/easiest/fastest lookahead are the steps where you can go faster, and the steps where you don't have too good lookahead are the steps where you should turn slower.
Hopefully this helps you out, most of my advice was based on the way I cube.