Rotating the dipstick to get it all the way into position is fairly common with a windage tray installation, at least based on my own experience. I put a 30 degree bend at the very end of the dipstick, probably 1/4" from the end or less, to help guide it past the windage tray. If you install the dipstick with that bend pointing away from the crank it will help get it past the windage tray.
The dipstick pushing out is a different situation altogether. There is lots of air movement in the crankcase, blowby or not, and if there is not enough breather capacity to let the pressure waves escape they will look for another outlet, hence the dipstick pushes out. Take a close look at your breathers; many of them only have two very small holes for ventilation of the crankcase, and these are not sufficient on a strong engine. An open, K&N style breather with a 1" or larger hole is a much better solution. Even if you have good breathers though this can still be a problem. On my 511" FE that I ran in 2005 and 2006, I put a spring between the dipstick handle and one of the oil filter adapter bolts, to hold the dipstick in position.