Finnish Syllabification

The Syllabification rule proposed in the Finnish Prosody example:

# Put a syllable boundary after a maximal expansion of the
# C* V+ C* pattern that is followed by a C V sequence.

define Syllabify C* V+ C* @-> ... "." || _ C V ;

is an approximation that works correctly for most short words. But the facts of Finnish are more complex. The nucleus of a syllable may not contain any number of vowels. It may consist of a

single vowel as the two syllables in ka.la 'fish',
a long vowel as the two syllables in riip.puu 'it hangs', or
a diphthong as the first two syllables of tie.toi.nen 'cognicient',

Any combination of these three basic types is possible in a word, e.g. sa.taa 'it rains', sa.toi 'it rained', saata 'accompany!', saatoin 'I accompanied', auta 'help!', auttaa 'to help'.

The definition of a long vowel is simple: any two adjacent identical vowels in the Finnish orthograpy make a long vowel. However, only certain non-identical vowel pairs constitute a diphthtong. The rules are:

A low (a, ä) or mid (e, o) vowel followed by a high (i, u, y) vowel constitutes a dipthong, for example, lai.va 'ship', lei.pä 'bred', häijy 'mean', kou.lu 'shool', köy.hä 'poor'. Certain combinations are ruled out by vowel harmony. The harmonizing low and mid back vowels (a, o) do not combine with the high front vowel y and the harmonizing low and mid front vowels (ä, ö) do not combine with the high back vowel u. There are no dipthongs ending in a low vowel. For example, the name "Lea" consists of two syllables: le.a.
The three high-mid sequences ie, uo, and yö constitute a dipththong when they occur in the first syllable of the word but not later in the word. For example vies.ti.en 'of the messages', tuo.te 'product, vir.tu.o.si.teet.ti 'virtuosity'.
Two-vowel sequences ending in i are always diphthongs, other sequences ending in a high vowel are diphthongs in the absence of a coda consonant, e.g. lak.kau.tan 'I cancel' but poik.ke.us 'exception'.

Your task is to modify the Finnish Prosody script to produce a defintion of Syllabification for Finnish that takes into account the above constraints on the nucleus of the syllable. Here is a set of inputs that it should syllabify correctly:

define FinnWords [{kala}|{riippuu}| {tietoinen}|{sataa}|{satoi}|{saata}|{saatoin}|{auta}|
                  {laiva}|{leipä}|{häijy}|{koulu}||{köyhä}|{lea}|{viestien}|{tuote}|
                  {virtuositeetti}|{laukaus}|{lakkautan}| {voimistelijoiden}|{heittäen}|
                  {heittäisin}|{laulaen}];