Try to focus more on F2L and find faster ways to do some cases that seem to take a long time. I have to agree that there's too many cube rotations and regrips. For F2L, insert pairs with R/U instead of R/F. Sometimes I insert with L/U or B/U if necessary. It just seems faster and doesn't require as many regrips/cube rotations.
Use your fingers more instead of using your whole hand (unless you are turning the R or L side) it seems awkward to me to use my whole hand to do an F/D/U move. Maybe practice doing algorithms that use R, U, and F moves and see how fast you can do it? When I started cubing I was doing the same thing until I figured out a faster way to execute algorithms. For example, your D2 was done with your whole hand. It would probably be faster after some practice to use your pinkie and/or ring finger to do the D2 move. Fingers move faster than your hole hand.