I have just found this thread, and I find it interesting because I see quite a lot of the problem that the OP first mentioned...under exposure (or over exposure often enough) from that damned histogram being over-trusted.
I can't add much to the excellent suggestions by a lot of regular contributors, but what I would suggest to anyone wanting to seriously learn how to cope with tricky lighting situations when you may be depending on accurate results that you take a look at Ansel Adams' Zone system, and understand why it works.
I had the good fortune to digest it and understand why it works so well many years ago just before spending a year in Antarctica where my main job was project photographer. And for those who have tried it, photographing in snow can lead to those same under-exposing problems the OP had. Of course that was in the days of film and Kodachrome II has little latitude, so I had to get it right....with no chimping either...Nikon Fs didn't have an LCD screen! Mine did have TTL metering, but I generally used an old Weston Master V with the zone numbers scratched on the dial as a reminder.
Because I understood the zone system I was able to expose that Kodachrome successfully, and could keep a check on my technique as I processed my B&Ws in the lab on base. During the summer I seldom saw the transparencies early than a month after taking the shots, and in the winter it was eight months!
The beauty of understanding the zone system even now is that the histogram takes on a completely new meaning, As has been so adequately pointed out, a perfectly centered histogram of a brides dress will give you a perfect mid (18% or zone 5) grey, which is hard to process. The zone system tells us that whites with textures belong in zone 8, three stops over exposed, and the bride's face, if she is Caucasian, belongs in zone 6. So get used to seeing the histogram leaning well to the right when photographing large light areas.
Of course, in the depths of a dark church you will be allowing the main BG to be dropping into zone 3 and 4....so always be aware of what is actually driving the exposure in your camera. Some folks prefer to spot meter, others to average, but if you practice enough with a system that works for you you'll soon see how it works. It's much easier to do than to describe! I notice that on my 5D3 my thumb has worn the paint off the metal around the top of the EC control!