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Comments

 * As an interesting note, when the following noun has been made definite
   but 

The suspense!

 I searched for quite some time on this subject, and only encountered
 papers covering that which I already learned; that Arabic has rather
 systematic subject pro-drop and object incorporation as pronouns, but
 I found nothing concerning the possibility for the type of Discourse
 related object drop we're interested in.

We're interested in the systematic kind too :-)

 As far as I can tell, subject prodrop is allowed with definite
 instantiation, and object prodrop is not allowed; it must be made
 up with pronoun incorporation (where the COG-ST is made explicit
 by the pronoun).

If you have access to a native (or near-native) speaker, I'd
be interested to know how they translate:

-- Are you hungry?
-- No, I've already eaten.

-- What do you do in your spare time?
-- I read.

 ...this latter case seems to be constrained to dropping the subject for
 activ-or-more. Furthermore, this seems to happen for all verbs, so I added
 OPT-CS activ-or-more to the verb-lex's SUBJ constraints.

The current implementation of basic-head-opt-subj-phrase doesn't actually
reference OPT-CS in the way that basic-head-opt-comp-phrase does.  It's
rather brazenly stamping [ COG-ST in-foc ] on the erstwhile subject.
I think you're right that I should allow for cross-linguistic variation
here, and even if I don't, [ COG-ST in-foc ] is too strong.

 Broken:

 I haven't investigated thoroughly, but it seems when I try incorporating
 both the direct and indirect object

??

 ** Something I still haven't figured out, however, is when generating I
 get extra parses which seem to take definiteness and case as optional
 on adjectives, but not nouns.

Provide examples when you make comments like this so I can take
a look...

 adverb-lex := basic-adverb-lex & intersective-mod-lex &
   [ SYNSEM [ LOCAL [ CAT [ HEAD.MOD < [ LOCAL.CAT.HEAD verb ] >,
	 		   VAL [ SPR < >,
		 		 SUBJ < >,
			 	 COMPS < >,
				 SPEC < > ],
			   POSTHEAD + ] ] ] ].

This is overgenerating, since you're allowing it to attach to any
verbal constituent.