Not read all the replies, so some of this may have already been suggested ...
If you are having timing issues, just execute your unit turn early -- don't wait for the bounce. Start a unit turn AS or before the ball crosses the net and complete a
full turn before the ball has crossed the back service line. Leave your left hand on the racket for a while -- to complete that full turn (see the Kevin G vid below). This way the right arm will not take over too early.
Now Macci might say that you don't want an early racket prep. At least he did some years back. He indicated that rhythm was important. Don't know if he still regards early racket prep as a myth. But, if you have timing issues, my take is to execute an early unit turn. If you execute as Kevin G does below, you can still have a very good rhythm for the rest of stroke -- and the timing will be much easier.
If, as you say, you can do this with shadow swings, but not with a live ball, then go with a progression. Start off with the shadow swings and then do it with very easy feeds (or self feeds). Progress to feed from a moderate distance and then to feeds from across the net. Work you way up to a feed from the opposite baseline, making sure that you execute an early unit turn and find the proper timing for the rest of your stroke.