Horizontal handlebars on a trike?
We need a picture of your setup. I've owned three trikes over the past 19 years and all of them had the handlebars designed so the part you grip is up, not horizontal. I can't see how I could get a comfortable grip on a horizontal bar. It is a real simple grip on one that is vertical or nearly vertical. I looked at my old Greenspeed GTO and the grip part of the bars are almost 90 degrees to the ground. On my Catrike 700 the grip is angled back toward the seat and that is a fixed angle designed by Catrike. You can't change the angle because Catrike uses direct steering. The only option is to move the grips closer to or further away from the seat. Handlebar position on Catrike 700 and Greenspeed GTO - see pictures below.
https://i.postimg.cc/k4WPqBhn/IMG-0716-Reszed.jpg
https://i.postimg.cc/wTsmJDtQ/greenspeed-gto-red-lg.jpg
You shouldn't slide forward in the seat if it is properly set up and fitted correctly for your size. When I set the boom on all of my trikes I used the same idea as with a conventional bike. My leg should be nearly extended when the pedal is the furthest away. I never paid any attention to my actual x-seam except to order a trike in the right frame size when there was an option. Two of the three trikes have fixed seats. No adjustment to the seat angle. The first one was adjustable and I just experimented with seat angle until I found the most comfortable setting. If you are sliding forward, are you sure the boom is set correctly? The GTO has a fixed seat angle of 40 degrees while the CT 700 is 25 degrees. Both are comfortable and neither one has me sliding forward.
I'm not surprised that the trike feels different from riding a DF bike. The geometry is far different so the ride will be too. Sometimes you can make adjustments to the seat straps that will make going over bumps less stressful. You need to adjust them so you don't hit the frame but otherwise the adjustments are there to make the seat absorb more of the shock rather than transmit it to you. There is a trade off with tire pressure. The higher the pressure, the less effort it will take to pedal the trike but it also means the tires take up less shock from going over a bump. Too low a pressure and you risk getting pinch flats if you hit a bump or curb. I just choose my routes carefully, avoiding the worst roads and getting the best ride I can with no pinch flats.