I'll bet that with straight arms and a fully extended back you would be sitting bolt upright on your current bike, or perhaps even leaning back a bit.
The problem is to lengthen and lower the front of the cockpit enough to get a bit of forward lean. That would be by losing stem spacers, flipping the stem to negative rise, and possibly buying a longer stem. A flat, no-rise handlebar can also help. To counterbalance the forward shift of your center of gravity, slide the saddle back, and lower it a bit. This will also add to extending the reach, also.
As for your feet, we're pretty much stuck with them. Next bike, find one with a longer front center--that is, the distance from bottom bracket spindle to front axle.