What I'm imagining is Allens 5 gallon water bottles, the heating up in a box or old oven and then laying pieces onto a wooden grid that has the round shape and leaves the impressions of all the little squares. I'm not sure heating a plastic bottle would ever get the bottom outside ring to ever reanimate. Everything else would blow out and it would remain mostly the same shape. So no vacu form, just heat and pushing it into a form with a piece of wood or welding gloves. The end color is done with transparent paint for faux stain glass or tinted clear coat products. If you have a wooden form, like a half round cage arrangement it might just be a heat gun and gloves on sections of water bottle like Allen does in so many things. Hold your breath doing this, the world record is over 17 minutes.
Resin is not good for large pieces, it is very fragile without the mat woven into it and shatters worse than cheap glass. It looks to me like the origional might be resin and tissue paper but this wouldn't last long touching or moving things. It could be 2 part polyester like you cover a bar top with, still any liguid is going to have to be applied over saran wrap on a form or poured into a mold. The polyester resins are more elastic but both those options are kind of expensive. Every $30 of stuff only covers maybe half of one of those at some decent thickness, like two coats to be able to support itself.
Another fabulous post from the U.S.Department of Wild Imaginings, now in spectaclar stereo, sponsored by the Adhesives and Sealants Council, suggesting ways to stick things together since the 1800s. Not fabulous in a gay way. Your results may vary. Illinois residents add 8% sales tax. These posts have been made by professional post makers, do not try this type of posting on your own without extensive training, lovely assistants and a trusty clown horn.