Roy shouldn't have been able to meet Nyles in the scene after the credits started rolling.

Makes sense, I didn't think of it this way

Only in her reality.

I was thinking the same, but actually you just cleared it up for me, pbt - that was the push that made Nyles join her.

Sarah was lying about the goat! She believed the experiment would work but didn't have definitive proof. She lied to
convince Nyles to join her. She wanted to be with him too - and she didn't want to leave him doomed to the loop. I didn't think she was lying because what would be her motive?

They actually show her with the goat as she tells the story, which usually means it actually happened. I don't know if the writers were thinking that Sarah was lying - but this helps it make sense for me.

I agree.

No goat reappeared after her experiment concluded that her plan would work in some shape or form.

That Ray met an oblivious (new) Nyles contradicts this conclusion. He should have met no-one. So, it is a plot hole…

…. unless each loop is to a parallel reality. This means Nyles finally escaped to
a reality-time-line, and whatever Ray would escape to hereafter would be to another - they would never meet again. So when Nyles leaves, Ray loops into one where Nyles is just one of the others… this does not explain the missing goat, but it explains how she might not find the goat again…. it just seems missing, as in this loop is it over a few hills.

Incidentally, this, too, explains the dinosaurs. If each loop is to parallel timelines, few of those still have sauropods roaming.