How hard would it be for me, a guy with no carb experience, but decent mechanical experience, to tackle removing the old carb and installing a new one...possibly a Weber?
Removing the stock Mikuni is not difficult, but before you start make sure you drain the coolant down to the point that there is no more coolant coming out of the rubber bypass hose at the carburetor. The mikuni is heated by the engine coolant to prevent icing, so if you pull it without draining the coolant you'll dump coolant into the intake(not a good thing...). There are four main bolts holding the carburetor to the intake manifold, then you need to pull the throttle cable, 5 or 6 vacuum hoses(usually two on the back, 4 or 5 facing the drivers fender, and 1 on the front for the AAP), a line to the charcoal canister, and the electrical connection plug. Once all that is unhooked you can lift it straight away.
I don't have any advice on installing the Weber progressive conversion, but I would imagine most of the existing vacuum lines will be capped if you go this route. You won't need the AAP connection, and you probably cannot use the EGR valve. You probably cannot use the AC idle up solenoid. You would most definitely want something hooked to the vacuum advance for driveability reasons, and I don't know if your auto tranny needs a vacuum load signal for shifting or if it has a cable. Hopefully someone more knowledgeable can point you in the right direction if you go that route.
As far as the 'icing' I hear about with the weber conversion, if you can use the stock aircleaner, the hot-air door on the stock aircleaner should keep you from freezing up. If you dump the stock air cleaner I can see where the carb would have a tendency to ice up under high humidity conditions. Happens on the VW's all the time when people who haven't got a clue cut the pre-heat pipes off of the intake manifold.
Chris