Honestly, I think that pot is too small for even one sunflower, even a dwarf, but definitely no more than one. I have planted three dwarf sunflowers in 6 inch pots and those worked out quite well. You could try to gently dig up the extra plants and replant them with a nice slug of water. Better than just pitching them.

Should I transfer them now while they're seedlings? And when I do transfer them, should I try to separate them to give them more space? I'm worried about messing up the roots.

I've grown thousands of sunflowers, but don't have any experience with transplanting them.. They seem to have a reputation for not doing well, but I've also read quite a few reports of them doing fine. I'd probably wet them down really well and carefully separate each seedling, replanting into bigger pots. No guarantees, though.

Don't worry, you can easily transplant them out. Pop out the soil block (I usually do this when the soil is fairly dry), use your fingers to loosen the soil (by doing this the seedlings tend to fall apart from one another), and gently take each seedling by the stem and peel them away from the soil and the other seedlings. Seedlings are pretty tough. They may sulk a bit when put into their new container, but they will quickly bounce back.

I would transplant each into a 9 oz. SOLO cup, before transplanting again into their final home (their final home should be in a container AT LEAST 6" wide) . When you transplant bury the stem so only a couple of inches sticks out above the soil line. Leave the seedling in the cup for 1 1/2 weeks, then pop the plant and soil block out of the cup and plant into your final container.

Good luck!