Why couldn't you sew a couple of simple seams on the tie outs to keep everything in tact. As long as you have duct tape on both sides and a significant margin of duct tape before there is only plastic, I don't think you would have any problems with tear out.
I second the use of the sheet bend on the corners this works amazingly well. You just have to remember how to tie the knot if it comes loose. I have been doing this on a poly tarp for a number of years. The pebble idea also works well, I have used this in conjunction with a continuous ridgeline to keep the ridgeline taunt and to provide extra tie out points on long edges. Simple, cheap, effective and surprisingly durable.
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