I will try to attach a pic. The pic shows the saddle tilted up at the nose but it was not comfortabe at that angle. It is an old old Brooks saddle bought at a Schwinn dealer about 1970. It has been on 3 bikes through the years.
I think your original idea, to shorten the reach, makes some sense.
Most saddles, I think including the B17, are intended for use near the level position. A tilt up of say 3 degrees is within the window. What you have there is a tilt more like 10 degrees. I can see where it is attempting to keep you from sliding forward.
I think with this small frame you are seeing the consequences of a not-too-good solution to the small frame problem. Small frames really don't have enough room for 700C or 27 inch wheels. To get the top tube in proportion with the seat tube (nearly equal), the front wheel moves backwards, coming close ot the downtube. There might be low clearance to the DT, and the toes will likely overlap the front wheel.
To fix this the head tube is inclined back, which requires a fork with low rake to get the trail where it should be. Some people don't like this sort of geometry. Good solutions are an artistic compromise.
The overall alternative is a long TT like you have. Combined with a laid back seat tube, it gives you a funky hip/back bend.
I'd suggest taking this bike to a good LBS for a fitting, or using some of the online guides like at Competitive Cycling.com, measure yourself and become analytical.
I suspect what will happen is that your hips need to come forward to get you in balance with respect to the pedals. This will reduce the tendency for your hips to pull forward on the saddle. To allow your hips to come forward, the saddle needs to come forward so it can still support your sit bones. This should also allow the saddle to come close to level, freeing up your pelvis to take a comfortable angle. Then you can really think about if your reach is right or not.
Road Fan