This would be Hothouse, written by Brian Aldiss in 1962. The novel was originally serialized in The Magazine of Fantasy and Science Fiction and was released in the US as an abridged version at first, called The Long Afternoon of Earth.
There is a plethora of evolved animal-like plants existing in a far future, tidally locked Earth that has become a massive jungle. The future form of humanity is tiny and green-skinned. The transparent seed casings you remember are carried entirely away from earth to the moon by mobile spider plants, and the people who seal themselves within them do undergo something of an angelic transformation, though it is described as a mutation caused by space radiation. One particular twist that I remember, though the Wikipedia article does not mention it, is that
The 'morel', a fungus that boosts the intelligence of the rider it parasitizes, once commonly inhabited all humans, which accounted for their comparitively high intelligence in the distant past. The character Gren learns this while in communication with the morel that occupies him.
The book has been reissued periodically, with the most recent edition in 2008-9, and was adapted into a comic called Hom.