Where are you at in your back lever progression?
I feel the core strength in back lever is the most similar to that required in a planche. Also, lowering into the back lever is similar in the fact that you have to "lean" forward - not open up your shoulder angle too much, which allows your shoulders travel forward. That allows you to progress out of the tuck into the straddle without throwing off your balance.
You can only progress so far just pushing with upper body strength. At some point the strength is there, but the balance must be developed.
Also, have you tried lowering into a full or straddle planche with a spotter?