Well, I reached out for some advise on the Message Board, and they had some good information. I thought it was good anyway, and started to tap out the screws. Well, I broke two 3/16" bits and ended up getting frustrated. But a pictorial version of my steps are as follows:
Step 1, swear at the door latch.
Step 2, remember that a friend bought you bolt/screw extractor set (that you put in the back of the tool box because you didn't really think that they'd work.)
Step 3, select a shiny, never been used 5 year old tool that hasn't ever been out of the case but looks like it'll slip down into the phillips screw recess with a partially wallowed out 3/16" hole.
Step 4, find the big-arsed crescent wrench and a pair if vise-grips and twist.
Step 5, place door latch assembly gently on table so as not to find yourself spending $50 to order a replacement.
Step 6, offer the old door a humble apology.
Step 7, have a beer, because I actually accomplished something today.