Use a CMOS 555 instead of the bipolar version. The bipolar 555 output won't swing to the positive rail, so it screws up the duty cycle. The CMOS part can't source/sink as much current, so you might want to change the 4.7k to 47k or more (the CMOS 555 still doesn't have symmetrical pull up/pull down capability), and lose the LEDs or drive them with some emitter followers or some other arrangement. Your duty cycle should get closer to 50%.
Alternately (or in addition), you could put a pot in your "synthesized ground" divider, but the bipolar 555 output level is still somewhat sensitive to temperature.
Alternately (or in addition), you could put a pot in your "synthesized ground" divider, but the bipolar 555 output level is still somewhat sensitive to temperature.