Do you have a video we can watch? That would be helpful.
Absent a video, I have a couple more questions.
Suppose we split the skill in half. The first half is getting from a straddle support to a straddle stand, and the second is getting from a straddle stand to a handstand. Which of those two halves are you struggling with?
How's your straddle pancake and middle split flexibility? Strength and flexibility can compensate for each other in a press; ie, the more flexible you are the less strength you need, and the stronger you are the less flexibility you need. But the technique might change depending on how strong/flexible you are. The simplified version is that the less flexible you are in the hips, the more your shoulders will have to lean forward past the hands to accomplish the press.
From what you said so far, my best guess is that it's at least one of two things:
1) you are not keeping your straddle compressed enough, and your feet are getting too far back too early. If this is the case, the solution is (somewhat counterintuitively) to keep your feet pushed forward as far as you can for as long as you can
2) you are not leaning your shoulders far enough forward, likely due to a lack of strength or confidence. If this is the case, the best drill I can recommend is to do a wall handstand (belly towards the wall) with your hands 6-18 inches away from the wall, and see how far forward you can lean your shoulders past the hands without falling. Experiment with different distances between the hands and the wall. Practice leaning the shoulders forward until the feet come off the wall, then try to get to handstand from there.