In other words, it sounds as if you've hit the limitation perimeter of the Betamid ($98), a single-wall, single-pole, floor-less tent that saves a bunch of weight (it's just over two pounds) but forces you to do without some niceties. Add the optional floor, and you're close to four pounds, which is close to tent weight.
The only other option, as you suggest, is to add a sleeping-bag cover. The best bet would be a simple Gore-Tex bivy bag, such as Outdoor Research's Standard Bivy Sack. But that weighs as much as the Betamid floor, and is expensive at $230. A good option: Mountain Hardwear makes a bag cover out of the same Conduit fabric that already wraps your bag. It's called the Conduit SL Bivy, and costs a more reasonable $109. The drawback: Two waterproof layers right next to you, which are apt to trap moisture inside the bag, or between the bag shell and bivy. And that could be bad, depending on conditions.
Bottom line: It's hard to find a place where price, weight and performance all intersect as neatly as you might desire. I suppose you always could by some 4 mil plastic poly sheeting, cut an 8X8-foot chunk, and wrap yourself in that when it gets nasty. That's what campers did in the good ol' days after World War II - take a chunk of military surplus waterproof sail cloth, and roll up in it when the rain fell.