Some thoughts on a simplified approach to ancient Greek grammar using only personal constructions. Since, both Infinitive and Participle constructions can be written as personal clauses with subordinating conjunctions, study of their syntax can be postponed.

Cover the 90% of greek verb morphology while ignoring the exceptions and rare. Instead of 6 principle parts, each verb has an imperfective and aorist stem via their infinitive. Regular verbs form the aorist from the imperfect by adding (s)a. Irregular verbs have an aorist reduced in some way from imperfect or an irregular form.
Past indicative has obligatory augment, either for carrying the stress or for disambiguating the 1st and 2nd plural.

Active endings for use when there is no returned action on subject (either partial or even figurative/implied)

PRESENT TENSES: after consonants or a/e/o uncontracted vowel stems (contains theme vowel): o^ eis ei omen ete onti
after vowels: mi si ti men te nti (not ousi)

PAST TENSES: after consonants (contains theme vowel): on es e omen ete on
after vowels: n s - men te n (all strong root aorists lengthen vowel)

IMPERATIVE: -(e) and -(e)te, etc

Medio-passive endings for use when there is either partial/implied returned action on subject or complete (reflexive); or subject receive action from (named) agent.

PRESENT TENSES: after consonants (contains theme vowel): omai esai etai ometha esthe ontai
after vowels: (remove theme vowel)

PAST TENSES: after consonants (contains theme vowel): ome^n eso eto ometha esthe onto
after vowels: (remove theme vowel)

IMPERATIVE: ?

SUBJUNCTIVE always uses the lengthened theme vowel endings (absorbs any stem vowel), OPTATIVE uses the stem plus iota plus the past endings without augment.

Example: te/mnein (regular aorist in -sa following rules, since there is no aorist form)
MinfVaAi te/mnein ; MparVaAi  te/mno^n
MimpVaAi: te/mne te/mneto^ te/mnete te/mnonto^n; (no past imperative)
MindVaAi: te/mn-o^ eis ei omen ete onti; e/temn-on es e omen ete on
MconVaAi: te/mn-o^ e^s e^ o^men e^te o^nti; te/mnoin ois oi oimen oite oin;
MimpVmpAi: ?
MindVmpAi: te/mnomai esai etai ometha esthe ontai; e/temnon es e omen ete on
MconVmpAi: te/mno^ e^s e^ o^men e^te o^nti; te/mnoin ois oi oimen oite oin

MinfVaAi tei/nai ; MparVaAi  tei/nas
MimpVaAa: tei/na tei/nate; --
MindVaAa: tei/nami.. ; e/teina  (present is not used in writing)
MconVaAi: tei/no^.. ; tai/naimi
MimpVmpAa: tei/naso teina/stho^ tai/nasthe teina/stho^n; (no past imperative)
MindVmpAa: tei/namai.. ; e/teiname^n  (present is not used in writing)
MconVmpAi: tei/no^mai.. ; tai/naime^n

POSTPONE AORIST PASSIVE DISTINCT FROM MIDDLE
FUTURE  is conjunctive, POSTPONE COMPLETE FUTURE SYSTEM UNTIL AORIST PASSIVE
PERFECT is with Perfect participle (redup + ko^s/kot-)  and einai.

IMPERSONAL CONSTRUCTIONS WITH INFINITIVE AND PARTICIPLE
learned as translations from personal subordinate clauses later
literature constantly footnoted until these are learned

Infinitives as hoti clauses when possible, nouns otherwise: need a way to automate this

• Subject: “συμφέρει αὐτοῖς φίλους εἶναι”  it is for their interest to be friends. it is for their interest that they be friends.
• Object: “παίδευσις καλὴ διδάσκει χρῆσθαι νόμοις” a good education teaches to obey laws. a good education teaches that one should obey laws. (ACI)
• Indirect Discourse: “ἔφη ἄξειν Λακεδαιμονίους” he said to be about to bring the Lacedaemonians. he said that he would bring the Lacedaemonians.
• Purpose: “παρέχω ἐμαυτὸν ἐρωτᾶν”  I offer myself to be questioned. I offer myself that I should be questioned.
• Result: “ἔχω τριή̀ρεις ὥστε ἑλεῖν τὸ ἐκείνων πλοῖον” I have triremes (so as) to catch their vessel. I have triremes (so) that I may catch their vessel.
• Absolute (Parenthetical): “ἀληθές γε ὡς ἔπος εἰπεῖν οὐδὲν εἰρήκασιν” not one word of truth, so to say, did they utter. not one word of truth, I may say, did they utter. 
• Exclamatory: “ἐμὲ παθεῖν τάδε” ; me to suffer this! that I should suffer this!
• Wishes: “ἐκγενέσθαι μοι Ἀθηναίους τείσασθαι” ; that it be granted to me to punish the Athenians! that it be granted to me that I may punish the Athenians!

• Imperative: “τοὺς χόας πίνειν” ; (to) drink the Pitchers! drink the Pitchers!
• Articular Infinitive: The infinitive can be used with the article as if it were a noun. “ἀνίη καὶ τὸ φυλάσσειν” ; to watch is also trouble
• Complementary: “δεινὸς λέγειν, κακὸς βιῶναι” skilled in speaking, evil in life. ??

Participles as hoti (adj) or epeide^,hote,kaiper (adv) clauses, with the verb in 3rd person and number taken from the participle, disregarding the case and number.

• Attributive: “ὁ ἐφεστηκὼς κίνδυνος τῇ πόλει”  the danger impending over the State. the danger that has impended over the state
• Circumstantial - Temporal: “ἀκούσασι τοῖς στρατηγοῖς ταῦτα ἔδοξε τὸ στράτευμα συναγαγεῖν” on hearing this it seemed best to the generals to collect the troops. when they heard ..
• Circumstantial - Cause: “οἱ Κόλχοι, ἅτε ἐκπεπτωκότες τῶν οἰκιῶν, πολλοὶ ἦσαν ἁθρόοι” the Colchians, driven out of their houses, were now gathered. the Colchians, since they had been driven out of their houses, were now gathered.
  “ἐθανατώθη ὡς ἀπειθῶν” he was condemned to death on the ground of disobedience, because he was disobedient
  
• Circumstantial - Purpose: “προπέμψαντες κήρυκα πόλεμον προεροῦντα” having sent a herald in advance to proclaim war, so that he would proclaim war
  
• Circumstantial - Concession: “πολλοὶ γὰρ ὄντες εὐγενεῖς εἰσιν κακοί”  for many, albeit noble by birth, are ignoble, although they are noble
  
• Circumstantial - Condition: “σὺ δὲ κλύων εἴσει τάχα” but listening you shall soon know, but if you listen you shall soon know
  
• Ablative Absolute: “τοῦτο δὲ λέγοντος αὐτοῦ πτάρνυταί τις” with him saying this, someone sneezed, while he was saying this, someone sneezed
  
• Accusative Absolute: “δόξαν δὲ ταῦτα ἐκήρυξαν οὕτω ποιεῖν” Having decided this, they proclaimed that they should do so, after he decided this..
  
• Indirect Discourse: “μέμνημαι Κριτίᾳ τῷδε ξυνόντα σε” I remember you being in company with Critias here (ACI) I remember that you were in company with Critias here

• Supplementary Participle: verbs of beginning and ceasing and λανψάνω, φψάνω and τυγχάνω. “ἄριστα τυγχάνουσι πράξαντες” they happen to have fared the best ??
• Circumstantial - Manner: “παρήλαυνον τεταγμένοι” they marched past in order ??
• Circumstantial - Means: “λῃζόμενοι ξῶσι” they live by pillaging. ??