When you flipped the stem you probably should have moved the seat forward just a tad about 5mm. If you need to push the nose down you're probably not sitting far enough back on the saddle. The rear of the saddle should be very close to your butt contact point. It seems a bit contradictory but this way you support your weight on your 'sit bones' avoiding the rising saddle nose altogether and easing the burden on your urethra.
It takes practice to be able to sit on the right, most comfy part of the seat and not on the nose where it hurts, but it's worth it. A bit like riding with your arms relaxed and bent to get you down lower.

I've only today raised the front of my seat on the race bike. I usually have it roughly level with a slight rise toward the front but I find that I can't sit back without using my arms to stop me from slipping forward onto the nose. Now I automatically slide back to the comfy part and there's less weight on my arms.

Because this is a most critical adjustment I'm now thinking I need a 'micro adjust' saddle clamp with two locking bolts to get the angle exactly right. Those serations on the seat clamp slide are not accurate enough, i.e. one notch is too far up or down.