Are you suggesting to work the negative portion of the straight arm press for the time being?
At first, yes.
The bent arm press to handstand from a frog stand is a nice parlor trick but easy. I'm sure my fat ass can still do it. Work the wall presses. You can do the seated pike and straddle holds and lift in the warmup. 3-5 holds of 10s, 3 sets of 5-15 lifts. Find something that is manageable. Try it 3x so long as it's not crushing you, especially since you don't want it crushing your FL work. 1-2m of L-sit and straddle-L can affect the quality of your FL work later on.
Try doing 5-10 holds of ring HS. 15-20s or so long as form is excellent and it's not crushing you. Remember, leave some in the tank.