Since learning the adjective + 得很 rule I have only seen it once in writing with a two syllable adjective。 What are the differences in register and／or meaning between 很 + adjective and adjective+得很？
I am not a linguist. As Chinese is my first language, I can describe how I use these 2 words. 很is like English word 'very', its place in a sentence is aways before another adjective. While 得很 is more intense, and it usually follows another adjective. For example: a, 这件东西很好。b,这件东西好得很。Both sentence a and b mean 'This thing is very good.', but sentence b is stronger in feelings.
很 + adjective can be followed by nouns, but adjective + 得很 can not.
For example: 很高的山峰
But we don't say: 高得很的山峰. It is just wrong.
I would say adjective + 得很 alomst always comes (with or without modal particle) at the end of a sentence.
这屋子 脏得很 。
你的字， 好得很嘛 。你怎么说不好呢？