"Is there any risk that the stored materials of the big synthetic yurt might have perished because they haven't been used? The storage is good, dry, and free of rodents. All in original crates it was shipped in."
Highly unlikely anything happened to it as long as the storage is as you say.
"I'm concerned about heating
a 30' as it has soooo much more volume than a 24'. Planning to use a log burner but worried I'll be waiting 1.5 hours to warm up and dry the space?"
It does take a while to heat, true, but once heated it will operate similar to a 24' in that you just maintain the temperature.
"How different are the acoustic qualities of these different materials sets? I haven't yet had a chance to stay in a modern material yurt but I've read a little and I can certainly imagine how the synthetic lining and insulation
would create a much less pleasant acoustic space. I know both will be loud when it rains and blows etc but I can't get it out of my head that I'll be lying in bed listening to the breeze and instead hear crinkling plastic."
I never hear crinkling plastic in my 30' Pacific Yurt. The vinyl roof is rather heavy which lends it to be quite stable. The walls are poly, and you can carry on a conversation with someone on the other side.
"Feel of the space with synthetic materials? Similar to above about sound but general vibe feel. I know what it's like to be surrounded in natural materials like wool and canvas. It's gorgeous. That plus the ecological impact of the modern style have me weary of the big yurt option..."
"Feel" is a bit of a subjective term, but I feel wonderful in mine.

Keep in mind that there is a fabric liner between you and the roofing material. You don't see the vinyl or poly.
I will say that the vinyl holds up like a champ. I wash the eaves each Spring and am always amazed how it all just looks so brand new when I am done, considering the yurt is 10 years old! I am a person with a limited amount of time so whatever I can do to reduce maintenance time, I do. A cotton canvas of any kind is going to require a bit of work, every year and especially every 5 years or so when you will have to replace it most likely. That was a big issue for me when I was deciding.