A word for a text with meanings read in both directions? [duplicate]

Solution 1:

They are still called palindromes, but are qualified by the term word-unit.

There are also word-unit palindromes in which the unit of reversal is the word ("Is it crazy how saying sentences backwards creates backwards sentences saying how crazy it is?"). Word-unit palindromes were made popular in the recreational linguistics community by J. A. Lindon in the 1960s. Occasional examples in English were created in the 19th century. Several in French and Latin date to the Middle Ages. - wikipedia

Solution 2:

Chiasmus, would be my response.

Taken from literarydevices.net:

Chiasmus is a rhetorical device in which two or more clauses are balanced against each other by the reversal of their structures in order to produce an artistic effect.
Let us try to understand chiasmus with the help of an example:

“Never let a Fool Kiss You or a Kiss Fool You.”

So in the example above, 'fool' and 'kiss' swap positions as noun and verb from the first usage to the second.

Incidentally, this is also a great example of zeugma.

In the OPs example, the first clause is mirrored in the second clause with the connective 'and' marking the mid point.

Solution 3:

The Dictionary of Wordplay by Dave Morice (2001, Teachers & Writers Collaborative) defines the term "word-unit palindrome" as you noted in the question. He also states that this type of palindrome is called a "pseudodrome."