Thanks. I thought I had already set that, but it must have been on a different test. Then I couldn't find how to set it; I was looking at the package I was testing, but I see now it has to be set at the Project level in Solution Explorer, and the Debugging tab is in Configuration Properties.
Having set 64bit to False, debugging works rather better - but I'm still getting these messages which state that it's running in 64 bit mode. Very odd.