Victor-
I haven't messed around too intimately with drive shafts, have no idea about the set screw that snapped on you. But when you snap a set screw on anything the normal "machinist's" procedure is to get a good carbide or cobalt bit (stronger than regular bits) and drill a hole down the middle of the set screw, then insert an "EasyOut" (any auto parts supplier should have these) into the hole. It screws in with reverse threads and as you keep "screwing it in" it eventually brings the rest of the set screw out. Soaking in penetrant oil before hand will help. If you can't use an EasyOut you'll have to drill out the set screw completely, then use a tap to cut new threads and replace it with a larger one. The main bolts on the flange should be bigger and stronger, soak them with penetrating oil, repeat daily until you're out of patience, try a wrench until you think it is unreasonably hard. My last resort weapon for "stuck screws and bolts" is a CO2 extinguisher. You freeze them down good instead of using a torch on them, it works better and doesn't hurt the metal. If you can borrow a 5 or 10lb. CO2 bottle they cost about $1-2 per pound to refill. Be careful working with it if you do: The CO2 in a confined space makes breathing impossible. You're trying to freeze something, so beware freezing your hands or eyeballs. And it is noisy as all hell, a bit scary to use the first time. But on the bright side you can't set the boat on fire, or de-temper anything metal! And you can always keep the CO2 bottle on the boat as an extra extinguisher.

Victor
You've had lots of good advice, but I might just add a bit. If you don't have access to the "slide hammer for extracting the shaft form the drive shaft flange, I have another technique that works very well. Loosen the flange bolts, and separate the flanges sufficiently to insert a socket in between the two flange parts, Choose a socket whose outside diameter is just a little smaller than your shaft diameter. Now as you tighten the flange bolts you will be pressing the shaft out of the flange. This works great,as I have used it many times on various boats. You might have to purchase slightly longer bolts to accomodate the added length when you insert the socket. If you don't want to use one of your sockets, any short shaft material of the appropriate diameter will also do.
Don Wagner

Victor,
Don's advice about the socket to push the shaft out is a good idea. I used that on my shaft last winter and it worked fine. Actually, I thought it was an original idea. And yes, I did wind up using longer bolts. It's a slow time consuming process, but it does work well. I would definitely recommend that you NOT use a slide hammer. You will be taking a significant chance of damaging the bearings in the output shaft of the transmission.
Good luck, Gary 'Expresso'

On drilling out the set screw, I agree that the easy out method can be risky. You are better off drilling the set screw out to the major thread diameter, i.e. 3/8" for a 3/8"-24UNF set screw, pull the shaft before undoing the coupling halves, then drill a new hole in the coupling and tap for the appropriate set screw. The added hole should be no problem, and I generally use two set screws set at 90 degrees anyway, as this is a much more secure arrangement.
On using a slide hammer to pull the shaft, don"t over due the pounding, as the transmission is not really designed to handle that type of in-line pounding. Better to make up a screw type puller, if possible, the heat the coupling and/or cool the shaft. If the worst case scenario develops and nothing comes loose, cut the shaft, use nut breakers on the coupling bolts, and buy new part.Rod