However F U F' and F U' F' are still far more awkward than R' F R F' for me.
For R' F R F', bring R' down with your wrist while flicking the F move with your pointer finger, then bring the R face back up for the R while flicking F' with your thumb. This can be done very quickly.
I know I don't have problem with R' F R F', my problem is F U F' and F U' F'. I presume you change hands between F and U.
F U F' is a pain in the rear, so don't worry about not feeling good about it. F U' F' is an easy right hand to left hand to right hand motion, using your right index, left index, and right thumb.
However, using your right thumb for F' is not always the best option. For example, take the N perm
R' U R U' R' F' U' F R U R' F R' F' R U' R
The first F' is easily performed with the right hand, as R' leads into it nicely and it is followed by a left hand motion. However, the last F' is rather poorly placed, as R U R' F R' wants to be one trigger instead of (R U R' F)(R' F'), plus the final three moves cannot be immediately performed (without some dexterity) after a right thumbed F'. So I taught myself to perform that F' with my left index finger, without taking my thumb off the front face (for stability).
This is like knowing when to perform R2 or R'2. They both accomplish the same same on the cube, but they differ drastically in how they affect your hand position, which is key in keeping your tps up.
You may want to do your F U F' as Bw L B'w, which is really the same thing, just a different way of thinking about it. And sometimes that's all it takes to make an awkward series useable.
Hope I helped.