Personally, I replaced caps lock with ctrl when you type and esc when you tap. ctrl, shift and alt are all vertically aligned that way so shortcuts are really easy in general.
I just don't use F keys, but for number I have a left thumb key that transform the right side into a num pad. You could do the same with functions keys. Or do what I did for any number and permanently remap the normal number positions to f keys as you said.
But the nice part is you get to adapt the keyboard to your own needs. If you only use one or two function keys, you could give them decicated buttons on the may layer. You can even have one button do the whole combo. For example I have one that does shift+insert so I can more easily copy into terminals.