Basically, the "agréer" verb translates as :
- Pronoun and verb or infinitive verb followed by a direct or indirect object : giving agreement/expressing convenience regarding the object. Example: "J'agrée à ses dires", "Ayant agréer les termes du contrat, ..."
- Non pronoun subject and verb followed by a direct or indirect object : subject gives an agreement/expresses convenience regarding the object. Example: "John agrée à cette condition", "Martin agrée les dires de Steven".
- Subject followed by a personal pronoun then verb : Subject pleases or is liked by the one designed by the personal pronoun or the one designed by the personal pronoun expresses liking / convenience regarding the subject. Example "Cela m'agrée", "Ce voyage t'agrée tant que ça ?" and indeed "Mes desiderata m'agréent.". Here, the personal pronoun gives a possessive means to the sentence and by this way gives to the verb "agréer" its original meanings expressing liking/convenience.
Thus, the invert for this verb in french has to keep the original meanings. In the case 3 and then your examples, it has to express the accordance with own (or subject) personal desire.
In the case "Mes desiderata m'agréent.", we have a subject "Mes desiderata", a possessive pronoun "m'" which means "to me / for me" and the verb.
The first step is to rephrase the sentence as it can be expressed in the form "Mes desiderata agréent à moi." where the personal pronoun become an indirect object.
The second step is then to conjugate the verb according to the indirect object as a subject : "J'agrée".
The last step is just to make the original subject as the new direct or indirect object : "J'agrée avec mes desiderata".