Hi Tropical! Cudos to you for doing your research! I had a very scary emergency with my Green Cheek Conure and the vet said her snuggle hut has to GO! I was horrified, I thought "what are you talking about lady, she LOVES her hut!" WRONG! It was then that I researched and learned all the dangers. Even if you inspect for frayed edges, you could leave to go to the store and come back and in that time your bird could have done enough new chewing to cause injury or death. OR, crop impaction can occur over time (your bird can ingest tiny fibers that you don't even notice missing and over time your bird can seem fine but all of a sudden when enough has built up, it is a very serious fatal emergency).
Huts have pros and cons, but here is what I believe is the safest in all aspects: Critters Choice small animal CHUBE.
They have various brands, but I use this one because I know of a bird lady who contacted the manufacturer and asked questions and felt it was 100% bird safe (also tons of parrot people have started using these and no issues). Kaytee also makes one but I don't know where theirs is made. I order the Critter's Choice Chube (made in the UK) on Amazon (size XLarge or Giant are perfect for Green Cheek Conures - they're not as big as you'd think so be sure to check the dimensions). Here's why I like these: they're made of safe vegetable parchment that's intended to be chewed (our GCC likes to sleep in hers and also has fun chewing one of the sides). They provide a "snuggle hut" type of bed without fabric dangers for crop impaction, strangulation or entanglement. They are not as fluffy/cozy as a traditional fabric hut so they don't resemble as much of a "nest" which can cause hormonal issues for your bird (hormonal behavior issues and also potential to become egg-bound) but they still provide a nice, SAFE place to sleep at night and feel secure. I will be a forever customer of CHUBES! Try it and please post what you think! Some people even drill holes in them and attach homemade toys. And no dangers of getting stuck in small holes like the seagrass mesh! Check out this website, it has a lot of useful info
Safe happy hut