Well, I may be a bit unusual in this regard, but here is what solved my "waking up with a backache problems". I would wake up every day with my back aching, and as the OP said, it would go away as the day went on, but it was really bothering me. I went to Sears and bought the best mattress my money could buy. I laid on it and it was so soft and giving, and it had a pillow top and I had to buy special "deep pocket" sheets because it was so thick and cushy.
My morning backache not only continued, but got worse. For the next 5 years I slept on the darn thing because it was SO expensive and I couldn't afford to experiment with another. Eventually I got divorced, moved, found a boyfriend and moved in with him. He had just purchased a new Tempurpedic and was very proud of it. The first few nights I was uncomfortable throughout the night and woke with horrible back pain, worse than ever before!!
So I told him I was sorry but I just couldn't sleep in his bed. We moved to the spare room where there was no bed at all. I set up blankets on the floor, sleeping on top of a comforter. I immediately noticed the morning back aches were GONE! For the first time in 10 years, I woke up pain free. My boyfriend got an idea, so we bought a platform bed that you would typically put a mattress on, but skip the box spring. But instead of a mattress, we went and bought one of those memory foam mattress "toppers" that are only like 2 or 3 inches thick. We figured, it was a cheap experiment since we could always add a mattress if we didn't like it.
Well, we LOVED it! Both of us. He had never complained about previous tempurpedic or regular mattresses, but said he felt a noticeable improvement with this. My pain was completely gone. Further more, to this day, when I lie down at night, I can actually feel my back 'self-adjust' against the firmness. So a 3 inch memory foam topper on a platform with no mattress or box spring is what worked for me.
My best friend is the opposite; the softer the better. So I realize every back is different, but I wanted to share my story because so often people just assume that "cushy & soft" is better for your back, and that is not necessarily so.