As for timing. The best period for sowing in a free farming way, in Holland, is in february and march. For several reasons this period has the best chances of yielding harvest. One reason is that harvest is only 4 months away, so the chance of the plot being bulldozered is minimal. Another reason is that in the previous months the weather is too cold for other weeds to geminate, so heaps of soil dumped in November still has very little other weeds (competition) growing in it in February.
So sowing in late april will be harder for the plants because weeds are all ready growing and have a head start. Even small seedlings of these will have at least a months worth of lead over you poppies. You plants probably will geminate but don’t really stand a chance to out grow the “enemy”.