Part of the confusion here is that the loss of the grammatical markers you note are a logical consequence of the the semantic use of incorporation.
An incorporated noun may be best compared, in my opinion, to a nonfinite verb, which will also typically lack much of the morphological features of a normal verb. This alone makes it evident why the standard markers a noun may present will usually be absent. Marianne Mithun describes four major reasons to incorporate a noun (quoting summary from Rosenfelder, Advanced Language Construction, pp. 182-184):
Narrow the focus of a verb by adding some sort of descriptor to it. You may want to incorporate tools, for example. In Nahuatl, such incorporation often translate to "X like (a) Y(s)".
Allow an otherwise oblique argument (usually of a semantically, if not syntactically labile verb) to become its subject (cf. English, "My head aches" vs. "I have a headache").
Background an argument that has already been mentioned.
Adding a classifier of some sort. This is an integral part of verbal morphology in the Algonquian Languages, for example. Chinese also does it to create suppletive forms of single-syllable verbs that may be highly polysemous or homophonous.
Add to this the fact that in most languages, you cannot incorporate the subject noun of an unergative verb (probably no language at all allow it, but I haven't looked into it in details), it is easy to see why incorporated/nonfinite nouns have little need for all the bells and whistles of regular arguments: you are either generalizing or backgrounding the noun, so you don't want or need to add these syntactic elements.
Regarding possessive markers specifically, I should point out that even in languages without incorporation, possessive markers are liable to be dropped if the possessor is already a separate argument in the sentence: I stole money from him, It struck him on the nose, J'ai mal à la tête, Je lui ai cassé le bras.
Finally, if a language has incorporation, it is usually rare for it to have a fully separate word category of adjectives as we understand them to begin with! In many of these languages, adjectives take the form of descriptive verbs or adjunct nouns that can themselves be incorporated into themain noun (cf. English Bluebeard, whiteboard, blackbird...), and syntactically, it doesn't typically work to incorporate an entire relative sentence.
However, some languages, such as Chukchi do allow for the whole noun+adjective phrase to be incorporated, and quite a few languages allow for numeral markers to be incorporated, although this is actually part of the verbal paradigm itself i.e. if you incorporate "I saw two persons" you are incorporating the noun "person" to a verb root that means "see two X", not incorporating "two men". That's what happens in Southern Tiwa or Algonquian languages (Nishnaabemwin: Giibimdaaswishiniizhdaabaan’gizwag, "They came in twelve carloads").
So, in summary, I would say aside from adjuncts noun and adjectives (which itself would make your language unusual, though not outside the realm of human experience), any other grammatical attribute of the noun you want to "incorporate" you should do so as an integral part of you verb paradigm, not as part of the incorporated root per se. If you are seeking a language that looks as natural as possible, anyway.