Picture posting is enabled for all :)
Last year I planted a row of Charlottes in size order, the largest was 2 to 3 times the size of the smallest, 25 tubers in all (the contents of a bag from B&Q).Whilst the largest broke the surface earlier that the smallest, there was no real difference in yield per plant compared to normal plant-to-plant variation.This is just one experiment mind, and I do chuck a load of chicken pellets and Poundland potato fertiliser in the trench when planting.But I don't think it makes as much difference as you think, compared to feeding and watering.
I have lots of large seed potatoes, is it O.K to cut them in half, if so do I cut them now as they are chitting or when I plant them.
In terms of disease caused by saved tubers I have reservations about this.I am of the opinion that if the crop was not diseased prior to saving then they should be OK as most potatoes are affected by soil borne or wind borne diseases on the plot.