In most cases, there is only 5-15mm difference in reach with the next smallest size. The frame is probably only one size larger than optimum, so it should be easy to change the stem to get the same reach as the next smaller size. If you have long legs and a short torso, then short reach bars may also be in order. Frame size has nothing to do with the relationship of the saddle to the crank. A smaller frame might have a steeper seat tube angle and permit the saddle to be placed a little further forward (a little over 1cm per degree), but it does not force a rider into a different postion. As a 5'-6" rider, with long legs (83cm cycling inseam and 73cm saddle height), most frames my size have a 74.5 degree STA. I use a seatpost with 32mm of setback, just so I can get the saddle back far enough.
There is no reason for the saddle to be positioned far forward, as shown. As others have noted, try the KOP method to start and if anything, move the saddle even further back to balance your body over the saddle. Getting some good cycling shorts is crucial, but so is some time in the saddle. Also, a comfortable saddle can be hard to find. Even after 25 seasons of riding, my crotch can't tolerate most of the saddles now on the market. I tried four different high-end saddles in one year and never found a real winner. Most are too flat. I need a saddle that's more round from side to side. The Fizik Gobi from several years ago (not the current model), is one of the best for me, but no longer made.