First, I've never had a problem with my beaded nymphs floating upside down, and I use down-eyed hooks - I'd be interested in hearing others' experiences with that. Possibly it has to do with the type of bead you buy. I might guess that beads with larger holes ridelower on the shank and thus keep the fly right-side-up? Also, perhaps using a heavier hook would help keep the fly upright.
When I wind wire over biots I wind it in the same direction as the biot, adding to the ribbing effect of the biot. Biots are slightly different shades on each side, so you can get two shades of flies from one strip of biots. I use regular dry-fly hooks (Tiemcos) because I'm too cheap to buy a lot of fancy hooks - they get pricey if you're buying decent ones, and it's much more important to have good quality hooks than a big variety. The mallard I was referring to is the speckled flank, and I would say every tier should have mallard flank in at least natural cream, natural golden, olive-dyed, and brown-dyed - phenomenal material for tails, legs, and wingcases.
When I tie in mallard for a wingcase, I attach about a dozen barbs by the middle of the barbs with a few hard wraps, measuring carefully so that the tips will become my legs (saves a step if you get the length just right). Then I half-hitch, push the bead back snug, and half-hitch in front of the bead, securing it in place by making a few hard turns (every turn I make when tying is hard, to be honest). Then I pull both the butts and tips of the mallard over the bead, tie it off with a few wraps at the head, and clip just the butts, not the tips. If I've been careful in my measurements, the tips can then be stroked back on either side of the bead and tied off, forming the legs without ever having to go through the maddening exercise of tying in two separate sets of legs. If you're going to mismeasure, let the tips be too long - you can always clip them shorter - they won't look as pretty to you, but they'll have a stronger profile in the water and the fish might actually see them better. Tying in slightly too many legs allows you to pull off any that misbehave or any extras - a lot easier than adding more after the fact. Finish the head and you're done. A word of caution to anyone wishing to follow this procedure: Plan more room for the head than usual. I don't think I've ever tied a fly with too much headroom, and I know I'm not alone. A somewhat large head on this fly not only preserves your sanity but also makes it more realistic looking by putting the bead in the thorax position (as Gonzo stated earlier) and making the legs look like they protrude from the proper place (funny, by looking at many flyshops' patterns, you'd think insects had 26 legs sticking out of their heads).
This fly is also nice in a grey color and a light brown. I've actually replaced many of these complicated biot ties in my flybox with a new and simpler pattern I've come up with, but I'll resist posting instructions for it as I hope to find a magazine editor dumb enough to publish them in return for a pittance.
Hope this helps.
-Shawn