As a former Corvette shop mechanic, I can tell you that most projects like this would be put on an hourly bid, meaning that you would be charged per hour instead of getting an estimated price. This is mostly because of the water and storm damage involved in the scenario. With this in mind, the job can get to be a bit spendy, as most Corvette shops have a minimum hourly rate of $90-$100.
That being said, every Corvette owner can help themselves by purchasing whats called the Marshall Guide, which is a book that lists the expected time that it would take an experienced mechanic to perform any repairs on most vehicles. That guide doesn't include extra details, such as vehicles with rust, water or other damage, but it does give you a good starting point.
Now, to give you an idea of what it would cost to get your u-joints and wheel barrings replaced if your vette did not have any special damages, you would be looking at a around $900 to start. That would cover at least 8 hours of labor of getting to each u-joint and then twp hours for replacing the wheel barrings. That price would not cover things like machining the u-joints if you decide to go that road. The price also doesn't cover parts, which would likely run you another couple hundred dollars or so, if you purchase them yourself and bring them to the shop where you are having the repairs done.
More than likely though, any shop that is worth it's weight in Corvette repairs, is going to charge you $1500 minimum for this job, just for labor. If you can find a shade-tree mechanic that you trust or you have a friend who doesn't mind helping you out, you might be able to get the job done for less. That being said, try to focus less on getting a low price and more on getting a mechanic who knows what they are doing. Corvettes are speciality cars and that requires a specialty mechanic unless you want to get more run-arounds and repairs.