Venus' escape velocity is just slightly less than that for Earth.
It's rotation period is 243 days. But its year is just under 225 days. The cursed planet takes more than a year to rotate.
It's a pure-blind cinch that a standard beanstalk won't work. That's why I'm suggesting a skyhook. Skyhooks operate in a variety of ways, but the key is that they don't go all the way to the ground, just dip into the atmosphere. Rotating skyhooks, by the way, are cool!
Back to the planet: I need to quote twice from my ancient atlas of the solar system.
"About 90 percent of the volume of the entire atmosphere lies between the surface and height of 28 km, and at this level the atmosphere resembles a massive ocean; it is dense and very sluggish in response to solar heating, which naturally is feeble at these depths."It goes on with further interesting details but my point is that for a balloon floating at about fifty klicks up, a geosynchronous satellite would be worse than useless.
"Without doubt one of the most surprising properties of Venus' atmosphere is the rapid rotation at cloud top level. The rotation period is only approximately four days, which is very fast when compared with the solid body rotation of 243 days."
Since the wind goes around the planet quite reliably at about a hundred hours, I propose linking the balloon to a similarly rotating position less than 150,000 klicks up.
Just as Arthur C. Clarke pointed out that between the moon orbiting at 28 days, and a satellite going around the Earth every ninety minutes, there had to be an orbital altitude where a satellite would go around the Earth in exactly twenty-four hours, and would appear to remain stationary to observers on the ground.
Well, to an observer in a balloon racing around the planet Venus, a satellite orbiting the planet at the same rate, ( a hundred hours), would also appear to be stationary.
Dropping a long tether from that satellite position may require a lot of carbon fiber or nano-tube bundles, but it is eminently doable.
Hmmmmn.
You have to be going a certain speed to "miss" Venus' horizon and stay in orbit. This isn't because of how fast Venus is rotating, but because of how much it "weighs". If you are going less than this speed, then you need some kind of thrust to counteract Venus' gravity. The Skyhook only works because it anchors a mass in ORBIT at orbital velocities.
If you are anchored to something in orbit cooking along at Mach 72, you will be getting dragged through the atmosphere at a decent percentage of that.
If you want to "float" along on the winds, you'll need to be running the motors on the Thrust ring almost constantly. Either that, or put your anchor mass BEYOND the LeGrange point so that it's outward inertia counteracts Venus' gravity well.
While pressure and temps at 50km from surface may be "comfy" for us human types, it'll still smell like rotted eggs.
Point of interest, at one point, Venus' rising in the morning was considered the "Morning Star". Also called, Lucifer...