Yeah I saw the reference to "drip tray" after I'd started making the post, but because I wasn't sure if you were talking about the same thing (because it's to stop drips going up rather than coming down 🙂) I still thought it was worth asking.
If you're not sure whether there's a correlation between it having been removed and the problem (you mentioned it but didn't say what you thought about it's effects) maybe try putting it back before driving in the rain, as a first step at least?
The wiper motors can use a lot more juice than the ones in newer cars (probably more than the lights), but if that's causing you to lose enough voltage to stall you, that probably tells someone who's a lot smarter than me about where you might start looking.
Being a 745L, it's carby rather than K-Jet isn't it?