Among the things you can try out with your next tarp is using 1" fiber reinforced strapping tape on all the edges and the ridge line. That will do a lot to keep if from stretching.
On the corners of mine I reinforced it with some 2" Gorilla Tape or clear fiber reinforced 3M Duct tape, and I put a grommet in the corners and the center of each side (also reinforced with tape) so I could tie them off or stake them down. I got an inexpensive grommet kit in the sewing section of Wal-Mart, and they have them at craft stores like Micheals too.
It is a bummer the visqueen is not clearer. And it gets hazier quick too as you use them. But even after a bit of use they're still great on moonlit nights, and I like that a lot.
You might try making a tarp out of a few SOL Emergency Blankets. They're made out of a tougher material that's not quite as stretchy and I think it's lighter than 2 mil visqueen. Plus, the reflective side offers some heat retention when turned towards you, and if you put it on the outside it reflects the heat from the sun in the hot months and keeps you cooler in it's shade.
I used a piece of bubble foil insulation under my sleeping bag when I slept in my hammock. It will slide around though. I never tried making a way to attach it so it wouldn't, but I don't think that'd be hard. It made a huge difference. As soon as I slid off of it I got cold.
You might want to try that as a floor for your tarp. Now I use a piece that's 40"x80" for the floor of my tent. I fold it in half both ways then roll it up. It rolls up into a 20"x5" roll and weighs about 17 ounces. (0.771 oz./ft²). A big tarp made out of SOL blankets taped together will weight less than a pound too, so that's a pretty sweet setup and both of those items are dual purpose. The floor can be folded and used as a sitting pad, or a ground cloth to lay yourself or your gear out on, and the tarp is already a big emergency blanket and giant signal mirror, so that's a pretty cool set up as far as I'm concerned.
We have lots of coyotes here too. I like them. There have been times when a pack has come up and started yipping and howling just a few dozen yards from my tent. They've never bothered me here or anywhere else so I don't worry about them getting into my stuff at all. I knew a guy in CA who told me a coyote saved his life by leading him back to his car after he got lost riding his dirt bike out in the desert. He said he thought it was going to eat him at first, but it kept walking towards him, sitting down, then getting up and walking away while stopping and looking back at him every few seconds. He finally started following him and about a half hour later he could see his car.
My wife, and a few of my neighbors swear they've seen a wolf around our places, but I haven't. I did see a TV show about "Coywolves" recently though, and they might have seen one of those. I wouldn't be at all surprised to learn they're here. They're in central and western Texas for sure and there've been a few wolves that have made it down here from Minnesota and one other northern state I think.
"You want to go where?"