OK, since two of you suggested to summarize what I'm uncertain about
specifically ... Ayeri is a VSO language, and I analyzed it previously
as having the following basic sentence structure for transitive
clauses where the subject NP is not a pronoun (view this email in a
fixed-width font to see the examples and charts lining up):

(1)              IP
        .--------+--------.
        |                 |
       ↑=↓               ↑=↓
        I'                S
    .---+---.         .---+---.
    |       |         |       |
   ↑=↓  ↓∈(↑ADJ)  (↑SUBJ)=↓  ↑=↓
    I      XP         NP      VP
                              |
                              |
                          (↑OBJ)=↓
                              NP

As I said in my original post, I analyzed my conlang's syntactic
structure in terms of LFG, so the c(onstituent)-structure tree above
contains functional annotations instead of relying solely on bar
levels in order to identify syntactic functions; non-branching
pre-terminal bar levels are moreover typically pruned for tidiness.
↑=↓ means that the semantic content of the current node is simply
passed on to (or actually, united with, as in set theory) the next
higher node; (↑SUBJ)=↓ identifies the current phrase as the superior
node's (and ultimately IP's) subject, etc.  This way, Ayeri relies on
an extended head for its verb (the head of VP is empty but its
functional equivalent is found as the head of IP), so that it is still
"configurational," also since I still c-commands V's modifiers this
way.

Now, the thing that is still puzzling me is that Ayeri very regularly
places modifiers after heads, and since there is no agreement
morphology on adjectives, adjectives follow their heads *immediately*
to keep scope unambiguous, even though they are adjuncts and not
complements.  Complements move up further to the right if an adjective
is present: NOUN--ADJ--COMP.  To give an example:

(2) Ang   vacya          John koyās   dano  gindiyēri.
    ang=  vac -ya    Ø=  John koya-as dano  gindi-ye-eri
    A.TOP=like-3SG.M TOP=John book-P  green poem -PL-INS
    'John, he likes the green book of poems.'

Here, the adjective _dano_ 'green' follows its head, _koyās_ 'book'
rather than the head + complement _koyās gindiyēri_ 'book of poems' to
signal that its head is 'book' rather than 'poems' ('*green poems' are
maybe the kind of poetry colorless green ideas prefer, I don't know).
Functionally, this construction should be in no way different from the
'normal' constituent order N--COMP--ADJ.  It's simply a quirk of Ayeri
to invert the order of complement and adjective/adverb, although as we
will see below, this quirk is motivated.

(3) +-                                   -+
    | PRED 'like <(↑SUBJ) (↑OBJ)>'        |
    |      +-           -+                |
    |      | PRED 'John' |                |
    | TOP  | PERS 3      |--.             |
    |      | NUM  SG     |  |             |
    |      | GEND M      |  |             |
    |      +-           -+  |             |
    | SUBJ -----------------'             |
    |      +-                          -+ |
    |      | PRED 'book <(↑COMP)>'      | |
    |      | ANIM +                     | |
    |      | CASE P                     | |
    |      |      +-            -+      | |
    |      |      | PRED 'poem'  |      | |
    |      | COMP | NUM  PL      |      | |
    | OBJ  |      | CASE INS     |      | |
    |      |      +-            -+      | |
    |      |      ,-                -.  | |
    |      |      | +-            -+ |  | |
    |      | ADJ <: | PRED 'green' | :> | |
    |      |      | +-            -+ |  | |
    |      |      '-                -'  | |
    |      +-                          -+ |
    +-                                   -+

Here, the part in question is the f(unctional)-structure labeled 'OBJ'
for its function as an object: its lexical head ('predicator') is
'book', which subcategorizes for a complement.  This requirement is
satisfied by the subordinate f-structure labeled 'COMP'.  The object
also contains an adjunct function (ADJ), and the only member of the
set is given as the adjective 'green'.  The question is now, however,
how to analyze this in terms of c-structure.  In LFG, functional heads
are regarded as co-heads of their equivalent lexical categories, which
is why I and V are regarded as functionally the same: both functional
and lexical heads of the same kind (verbal, nominal) write their
semantic features into the same f-structure.  The strategy of verbs
should thus in principle also be applicable to D and N, with D as NP's
extended head.  However, I have so far analyzed NPs with adjuncts and
complements in the following way and was wondering if this is correct:

(4)         NP
        .---+---.
        |       |
       ↑=↓  (↑COMP)=↓
        NP      NP
    .---+---.
    |       |
   ↑=↓   ↓∈(↑ADJ)
    N       AP

While it is generally possible to adjoin a phrasal node to a phrasal
node, the restriction according to LFG's annotation rules is that
phrasal nodes adjoined to another phrasal node either need to be
unannotated (I suppose, this means ↑=↓) or not to embody an argument
function, however, COMP *is* an argument function.  For nouns, I
suppose one could still invoke lexocentricity---the word as such
identifies the NP as a complement, here by way of its case marking.
This does not work for all phrase types, however, since e.g. CPs as
complements of predicative adjectives (nice [CP that you're here]) do
not mark case.  I was wondering therefore if the following analysis
might not actually be better, also because it parallels the way Ayeri
handles verbs:

(5)             DP
        .-------+-------.
        |               |
       ↑=↓             ↑=↓
        D'              NP
    .---+---.           |
    |       |           |
   ↑=↓   ↓∈(↑ADJ)   (↑COMP)=↓
    D       AP          NP

The head noun is found as a functional head D here, while N itself is
empty, however, its complement is still in place.  This parallels how
V is empty, while the object, as V's complement, is still constructed
as a daughter of VP.  This also allows for annotation of the nodes
according to the rules, or at least without bending them, as far as I
can tell.

A question arising from this is how to deal with determiners.  Since I
modeled my analysis in (1) on Bresnan et al.'s (2016) analysis of
Welsh---which they analyze as not using Spec as a parametric
choice---I implicitly assumed for Ayeri as well not to make use of
Spec.  This means that I analyzed determiners like _nā_ 'my' or
_sinya_ 'which' (as an interrogative pronoun) as heads of DP which are
complemented by an NP, as in (6a).  However, with the analysis in (5),
can I still follow this strategy and have [DP [DP NP]], as in (6b), or
is it preferred for DP not to recursively include another DP for some
reason? This is probably a Syntax 101 question, but I've never really
had a Syntax 101 class.

(6) a.         DP
           .---+---.
           |       |
          ↑=↓     ↑=↓
           NP      D
       .---+---.
       |       |
      ↑=↓   ↓∈(↑ADJ)
       N       AP

    b.                   DP
                   .-----+-----.
                   |           |
                  ↑=↓         ↑=↓
                   DP          D
           .-------+-------.
           |               |
          ↑=↓             ↑=↓
           D'              NP
       .---+---.           |
       |       |           |
      ↑=↓   ↓∈(↑ADJ)   (↑COMP)=↓
       D       AP          NP

I mentioned above that adjectives can have phrasal complements.  If an
adverb is present, complements of adjectives move up as well, but
adjective phrases do not have a functional equivalent. So what would I
do there, if the strategy outlined for nouns in (5) is followed
mutatis mutandis? Would I simply put an AP inside another AP, or would
I maybe rather use DP, since adjectives are a nominal category in my
conlang?

Regards
Carsten