I'm curious - what kind of CTR's are you getting on your landing pages when the traffic is sent from push ads? So how many people click through and go to the offer?
I'm used to very high CTR on Facebook traffic, well over 50%. Usually about 70%. But on push traffic I get around 10-15%. I've tried very short landers, longer ones, with images, without. I just can't crack 15%.
You use same type of lander as you used for FB? The traffic on push is frozen, you need to warm up it slowly. We still learn push (doing Ecom) and had short success but we mostly on negative ROI, yet... But after spending some money we learned that you need to add few steps.
I'll even split to 2 presell pages before offer, one with review videos or vsl and one with advertorial and only then to offer
I started with the same landers FB and then tried all different kinds I could think of. The problem I'm talking about is not even conversion but that nobody even clicks on the lander to go further.
What percent of people do you have clicking on the lander to go to the next step?
Depends on the vertical a lot too, and the GEO and the AD ... 
I've seen anything between 5% and 50%. It was easier to get high CTR with a bit suggestive dating LPs than with the more boring sweeps LPs... you get the idea.
Push traffic is really "cold" these users respond better to more intriguing content.
As said above, it really depends.
But if you need a number, my average is around 25-30%.