how can the deeply religious be convinced (or reassured) that accepting what science teaches does not require rejecting their faith?
Don't trouble the good doctor with this bogus question. I'm a deeply religions person who accepts what science teaches. Your mistake is assuming that all, or even most, people of faith are luddites who need convincing, like your aunts and uncles. In fact, most are not.
 http://www.gallup.com/poll/21814/Evolution-Creationism-Intelligent-Design.aspx
I know that I was talking about Yourg Earth Creationists and Gallup poll is about if God created mankind within the last 10,000 years and those are different questions. However, the poll does show a clear rejection of science by people of faith. As of the 2012 numbers, "God created man as is" was 46%, "Man evolved with God's guidance" was 32%, "Man evolved without God's influence" was 15%. If we assume (I know, I'm going out on a limb here) that the 15% are largely comprised of the atheists, agnostics, and various unaffiliated, then people who believe in God in the U.S. (another limb, but that's where I live) are more likely to reject than accept the science of human evolution by almost a 3:2 margin.
Among the deeply religious in the U.S., you sir, are in the minority if you accept the science of human evolution.
However, since the title of this article is "... Merging Science and Religion" I thought I would ask about a particular situation in my life where trying to merge religious beliefs with sciences as varied and accepted as plate techtonics, carbon dating (or potassium or uranium), paleontology, and astronomy failed. My cousin, who is home-schooling, asked me how I thought she could teach her children what they are required to know for state tests and stick to the dogma of her church. Of course the answer is obvious, but there are none so blind as those who will not see.