2 problems hit me right away with your "simple solution.
#1- How heavy is a mylar sheet the size of Texas? OK, so you say 1/10 the size of Texas? Thats gonna take a lot of delta rockets, and a lot of people sewing the mylar together.
and #2- (this is the big one), How do you get 1/3 of the atmospheric pressure of earth, when Mars is only 1/6th the size of Earth. Remember, atmospheric pressure is determined by the the gravity of the planet.
Well for that we need heavy-lift. I.e. something on the order of the Saturn V. Which is COMING with Ares V, provided that NASA isn't messed with as far as the budget goes. As far as the pressure goes, it's not about gravity. It's about density. If we heat the planet, we release the sequestered CO2 and H2O faster than the solar wind can strip away molecules from the top of the atmosphere. Then we've created a denser atmosphere, higher density, higher mass, higher pressure.
If it were ONLY about gravity, Mars would ALREADY have an atmospehre with 1/3 the pressure of MSL on Earth, because Mars gravity is 1/3g. And the moon would have a 1/6bar atmosphere. It doesn't work that way.