Although I am not a professional photographer, I take my photography seriously when I travel.
I took a 14-day Rome to Venice tour with my mother a few years ago, and all I took was a Panasonic LX7 and my iPhone. (Nowadays, I would pick an LX100 instead of an LX7.) Overall, it was liberating to travel that light, and I was pleased with my images. The thing is, a lot of days I walked 10+ miles, even though we went by bus from city to city. Sure, I missed some shots because the focal length was too short or the light was too low, but at the same time I got a lot of shots walking around that I would have missed if had been tied down with a lot of heavy gear.
On later trips, I have taken M4/3 gear, and I have found it to be a nice compromise between weight/size and functionality.
My recommendation would be to set a weight/size limit. What are you comfortable carrying for 10 miles or 10 hours without a break? For me, that limit is whatever I can cram into a Billingham Hadley Small -- usually two M4/3 bodies with two or three lenses, depending on the lens size. For you, the limit may be very different.
Overall, you need to cover the 24-70mm range really well, and you need some speed for churches and interiors. Something like a 24-70mm f2.8 or faster would be ideal. Everything else is optional. Occasionally it's nice to have some extra reach, but you can get by without it.
I generally do not bother with flashes or tripods for this kind of trip. Almost all churches and museums prohibit them.
A polarizing filter is good to have on hand, too.
Oh, and ditto what other folks have said. Make sure your camera shoots raw, and cables and batteries and accessories always take up more space that one expects.