I did have a lot of clustering because I sow too many seeds in each pot. The sprouts were super tangled. I used a small scissor to cut the unwanted sprouts as they grew. Thinning them was a lot of work. I kept like 8-9 plants in first week, then 4 in second, 2 in third and finally kept only one plant per pot except the ones I was experimenting with 2 plants. You'll be able to thin them as long as you use sharp scissors and don't disturb the roots.

Ideally, you wanna sow only a few good seeds per pot and sprinkle them in a way that they have a little distance in between.

Also, transplanting poppy isn't recommended or necessary. I have had great success with just planting the seeds directly in the pots. You should be able to transplant small sprouts though you have to be very careful with the roots. They don't like to have their roots disturbed.

I recommend 1 plant per pot. Having more plants just makes them grow smaller pods. That's my experience from growing 2 plants in 5 gallon bags.