Firstly, I think that there should be commas in the second clauses. However, the second sentence, to a British ear at least, sounds a bit unnatural. they deeply envy us' to get the meaning you're positing.
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David HattonYes, it seems to alter the 'deep down' from being relevant to 'I' to relevant to 'them'.I see, then let me ask - did both interpretations come to your mind when you were reading this sentence for the first time (without my suggestions as 1a and 1b)?