Yeah, I have encountered stuff like that. Mostly it is simply finding a more sheltered location. Unless you are on a flat, open plain, with no surrounding hills, you *will* find spots that are more sheltered than others.
Selecting a site can be difficult. Usually the eastern slopes just below a ridge or peak will give you some cover. You mention no trees, so the best I can do is equate that to a beach in a 50mph gale like storm. You mention no stakes, so good sized boulders or largish stationary boulders are your only option for tying off. Clearly, you need more of them, if they are being dragged 6'.
1) Get the tarp as close to the ground as possible. Closing off all air vents to the bottom will help a lot with the vacume pressure exerted by high speed winds. On the beach, I was using a 24" and 12" stick, nearly breathing in the tarp as it pressed down over me.
2) Keep whatever doors, corners, flaps anchored and closed. Letting in air can lift the tarp. Avoid that as much as possible. Tie off center lines *inside* if you have internal tie outs. You can hold these if necessary, but not sleep with them.
3) Keep minimal surface area in the wind. You might find diaganal orientations to be better than "square".
4) Add a wind break around your shelter. Even a single layer of 6-8" rocks and boulders can help.
6) Put a few on top of the tarp, if you have to. You can seal it later if it starts leaking; you need shelter *now*!
7) Dig a few inches into any sand with your foot. Ground friction will help reduce wind velocity, so, the closer to the ground you are, the better. Keep it inside, though, you don't want to puddle any water from rain.
8) Add double lines, diagonally across the shelter. Assuming you brought 100yd of light line, use it. Extra lines are painfull to set up and tear down, but better than getting wet or all sand. These will keep the tarp from billowing up. Extra tieouts on each loop will help. Extra tie outs in between (a pebble tied off works pretty well as a tarp anchor.) This will also reduce any air comming in the bottom, trying to billow the tarp up.
LOW and fairly well SEALED should let you survive a night of 40-50mph winds. Perhaps not comfortably, but OK. I mention a beach because this is common when paddling. The wind from the lake can be in your face at night and at your back in the morning. I try to set up at an angle to the winds, esp in spring and fall.
Worst case, You can simply roll in the tarp, keeping the edge down. You might have a bit of condensation, like a bivy, but you can get some sleep.
