Some sound advice. You will almost certainly help stabilise yourself with a good set of core-stability exercises. Try to avoid the classic crunches and back raises and go for balance/proprioceptive stuff as suggested by Charlie. Almost always, the larger abdominals and lumbar muscles are big and powerful enough, it is the deeper, smaller muscles acting to stabilise the hips and spine which get tired easily (especially as we tend to send them to sleep by sitting at desks and spending time in cars). Work on these and you'll eradicate the small movements and instability which is a popular cause for lower back pain.
Jameso: glad to hear that your problem was helped by the inline seatpost, although the reasoning is good, I wanted to help just explain what is really happening:
The steeper seattube angle brings the saddle further over the bottom bracket. This in itself doesn't allow you to get lower. What it does do is allow your pelvis to rotate slightly under you, thus shortening the distance your hamstrings are stretched over and taking some of the strain off them. Be careful however and make sure you keep stretching as eventually the hamstring tightness will catch up to the new position and you could be back to square one. Also make sure that your knee is nut pushed too far over the front of the pedal axle as this will put extra strain through the knee joint as you put the power down.
I'm not suggesting that your solution has not been a good one for yourself, just wanted to give you a bit more info so you don't lead yourself into different troubles in the future.
Find a good physio that understands how things work when you ride your bike.If you are based anywhere near Manchester, give me a shout (details all on website http://www.pedalprecision.com) and I'd be glad to take a look.
All the best,