shortening the stem affecting the handling is not about weight distribution, its about shrinking the arc that the bars make while turning that can make a smaller input have a greater output. I do not like to go below 80mm, as it gets to twitchy, and i dont like going past 120mm. If you get 80 and its still too long, try investing in some short reach drop bars.

moving your seat forward can impact your knees as it affects the relationship of the knee over pedal spindle. ideally if the seat tube of the bike is 73 degrees, when your pedals are at 3 and 9 oclock, the back of the patella on the forward leg should be directly above the pedal spindle. Every degree off of 73 is about 1.8cm forward or behind, depending. The goal of this is to have one pedaling straight down when at the most powerful part of pedal rotation, not pushing forward or backwards but up and down like a piston. Considering the bike is too big for you as is, i think switching to the zero setback will only help, as you're probably too far back now. Also it gets a bit fuzzier when you are using clips and straps, it is more important when you are riding clipless.

I would not switch the seatpost around, as many posts are designed to take loads in that direction, and you are putting yourself at risk to break it.