B&S Intek 20HP, first minor ticking, then rough running (like missing one cylinder), then mechanical clunk . . . now zero compression! What should I look at first? Can valves and valve gear be replaced without engine removal on ride-on mower?

You can replace the valves without removing the engine by removing the head first. The valves will come with it, however, the mechanical clunk isn't usually indicative of valve issues. I would remove the head, and push on the piston to see if you threw a rod instead. Sounds like the connecting rod was knocking, then gave way, and now the piston isn't moving at all. Another way to tell, is just to put a screwdriver in the spark plug hole, and turn the engine over by hand and see if the screwdriver moves. If not, you need to tear the engine down and fix your rod issue. If you're lucky, you may find the the end cap bolts came loose, and you can put it back together without too much issue. Otherwise, your engine's probably done.