I can whip, not perfect, but I can. Only flyout/downside over pyramids, not flat yet. I do goofy whips though so they're a lot harder for me.
But anyway, try flyout. They're much easier.
Sounds like you need to get your legs over, and to do that you just need to keep your weight over/push down on your bars. That'll keep your weight forward and allow the bike to swing around faster, while keeping everything under you.
I was in your position forever, and one day figured out to just step over and I was catching 1 foot. Was stuck like that for almost a year until my friend who has them dialed told me I need to push down on my bars just a littttle bit more, and I'd probably land them. and he was right because in like a week I landed one. So basically what I think you need to do, is just TRY to step over. It seems weird (for me at least) but just step over your frame, and to keep your weight over, tilt your bars (Tilt left side down, right side up if you're whipping clockwise, and vice-versa for counterclockwise) and go for your pedals.
You have it easy though and don't necessarily need to worry about stepping over as a big issue like I do since I do goofy whips, so you can probably get away with stepping just to your front foot while pushing down, and with some practice you'll figure it out. Can't really help much there since like I said, I do goofy whips haha.
So to review:
-do your whip flyout
-when it gets halfway around, tilt your bars down (left side of bars tilt down if you're whipping clockwise/right if counterclockwise)
-Step to your pedals, don't wait for them to come to you, go to them.
-land
Pretty much it.