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かふ (買ふ) | kō | [kʰò̞ᵝː] | (v.t.) "trade, exchange" — hints that h-row characters at the ends of words often indicate verbal endings: をたへ (wotae), すへ (sue), and をたへさく (wotaesaku) can consequently with some certainty be guessed to be verbal forms of some type. From this, it might be gathered that さく -saku is some sort of verbal marking. The Japanese cognate form is 買う (kau), also noting that words in -ō in Ineshîmé may correspond to words in -au in Japanese.
むさじい (兎) | musaji | [mʉ̀ᵝ.s̪ɐ̞́ˑ.ʑì] | (n.) "rabbit" (definite: むさじいけ (兎け) musajiki or むさじいは (兎は) musajiya) — this is probably cognate to Japanese 兎 usagi (same meaning, but it has a prothetic m-, hinting at the cognates to むくつ (mukutsu) and むそう (muso). Looking up this word would also reveal that it has a dialect form 兔 wasaji, and notes that nouns once having initial u- tended to either develop prothetic consonants, or to break into /wo/; the wa- in wasaji is probably a hypercorrection, some dialects having a more likely inherited form wosaji. This was probably too abstruse to actually work.
ざひ (不ひ) | zai | [z̪ɛi] | strong negational suffix, "never", "does not ever" — hints that ぜひ (zei) has a negative function.
ふるとうく (古期) | furutoku | [ɸʷʉ́ᵝ.ɾ̪ʉ̀ᵝ.t̪ʰó̞ᵝˑ.kʰʉ̀ᵝ] | (n.) "former times" (definite: ふるとうくゐ (古期ゐ) furutoki) — reveals there are multiple different sorts of definite inflections. Also introduces the spelling rule that a w character following an u-character is probably pronounced identically to whatever the base consonant was, followed by whatever the w-character vowel is (くゐ ku-wi is read as ki); this is a hint at とぶえ (tobe being some sort of inflection, though you might expect it to be spelled とぶゑ (to-bu-we) rather than とぶえ (to-bu-e).
ておい゙ (強) | tyol | [t̪ʰʲó̞ᵝɫ] | (adj.) "strong, forceful" — provides the spelling of terminal -l, noting also that it developed from an earlier /j/-like sound.
ゐり (居り) | yuri | [jýᵝˑ.ɾ̪ʲì] | (v.) "to be somewhere, to be in a place" — provides a hint at the shift of /wi we/ to /ju jo/.
ふくて (梟て) | fukute | [ɸʷʉ̀ᵝ.kʰʉ́ᵝˑ.t̪ʰè̞] | (n.) definite form of ふく (梟 | fuku | [ɸʷʉ́ᵝˑ.kʰʉ̀ᵝ] ) "owl" — note that this word is clearly onomatopoeic ("fuku" sounds like it could be an owl noise"; provides a hint that くぽくて kukkute is another onomatopoeic word with a similar meaning.
むさじい (兎) | musaji | [mʉ̀ᵝ.s̪ɐ̞́ˑ.ʑì] | (n.) "rabbit" (definite: むさじいけ (兎け) musajiki or むさじいは (兎は) musajiya) — this is probably cognate to Japanese 兎 usagi (same meaning, but it has a prothetic m-, hinting at the cognates to むくつ (mukutsu) and むそう (muso). Looking up this word would also reveal that it has a dialect form 兔 wasaji, and notes that nouns once having initial u- tended to either develop prothetic consonants, or to break into /wo/; the wa- in wasaji is probably a hypercorrection, some dialects having a more likely inherited form wosaji. This was probably too abstruse to actually work.
ざひ (不ひ) | zai | [z̪ɛi] | strong negational suffix, "never", "does not ever" — hints that ぜひ (zei) has a negative function.
ふるとうく (古期) | furutoku | [ɸʷʉ́ᵝ.ɾ̪ʉ̀ᵝ.t̪ʰó̞ᵝˑ.kʰʉ̀ᵝ] | (n.) "former times" (definite: ふるとうくゐ (古期ゐ) furutoki) — reveals there are multiple different sorts of definite inflections. Also introduces the spelling rule that a w character following an u-character is probably pronounced identically to whatever the base consonant was, followed by whatever the w-character vowel is (くゐ ku-wi is read as ki); this is a hint at とぶえ (tobe being some sort of inflection, though you might expect it to be spelled とぶゑ (to-bu-we) rather than とぶえ (to-bu-e).
ておい゙ (強) | tyol | [t̪ʰʲó̞ᵝɫ] | (adj.) "strong, forceful" — provides the spelling of terminal -l, noting also that it developed from an earlier /j/-like sound.
ゐり (居り) | yuri | [jýᵝˑ.ɾ̪ʲì] | (v.) "to be somewhere, to be in a place" — provides a hint at the shift of /wi we/ to /ju jo/.
ふくて (梟て) | fukute | [ɸʷʉ̀ᵝ.kʰʉ́ᵝˑ.t̪ʰè̞] | (n.) definite form of ふく (梟 | fuku | [ɸʷʉ́ᵝˑ.kʰʉ̀ᵝ] ) "owl" — note that this word is clearly onomatopoeic ("fuku" sounds like it could be an owl noise"; provides a hint that くぽくて kukkute is another onomatopoeic word with a similar meaning.
Next, the things that have been guessed so far:
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As has been already noted, を (wo, among other readings) is an accusative marker, の (no) is a relational marker, とう (tou) is a quotative, instrumental, and comitative marker. A few more oblique hints have been provided in my responses already. A spelling with o-u for a short-o is also conventional, not an indication of an etymological long vowel or diphthong.
いふれ (iyure) is an inflection of a verb meaning "speak, say, tell", normally 語れ. The word 語 on its own means "language".
すず (suzu) does not, in context, mean "bell", but it has a vaguely related meaning, and is written with the same character (鈴), compare 鈴 (gangan, usually a large, more European-looking bell), and 鈴 (jinjin, a small bell, as of a bicycle, and is usually not intended to be musical).
なつ (natsu) has undergone no semantic differentiation at all, and is simply 夏 "summer".
くっく (kukku) is an onomatopoeia. It is related to くぽくて (kukkute); the difference in spelling is conventional, not etymological.
いふれ (iyure) is an inflection of a verb meaning "speak, say, tell", normally 語れ. The word 語 on its own means "language".
すず (suzu) does not, in context, mean "bell", but it has a vaguely related meaning, and is written with the same character (鈴), compare 鈴 (gangan, usually a large, more European-looking bell), and 鈴 (jinjin, a small bell, as of a bicycle, and is usually not intended to be musical).
なつ (natsu) has undergone no semantic differentiation at all, and is simply 夏 "summer".
くっく (kukku) is an onomatopoeia. It is related to くぽくて (kukkute); the difference in spelling is conventional, not etymological.
Everything that's explicitly revealed would look like this if glossed:
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むくつ くぽくて をたへ とぶえ、
Mukutsu kukkute wotae tobe,
[mʉ̀ᵝ.kʰʉ́ˑ.t̪͡s̪ʰʲỳᵝ kʰʉ́k.kʰʉ́ˑ.t̪ʰè̞ wò̞ᵝ.t̪ʰɐ̞́ˑ.è̞ t̪ʰó̞ᵝˑ.bè̞]
SOMETHING SOMETHING.DEFINITE VERB.SOME-INFLECTION VERB.SOME-INFLECTION
ぜひ むそう よたよるゐを いふれ、
Zei muso yotayori wo iyure,
[z̪ê̞ː mʉ́ˑ.s̪ò̞ᵝ jò.t̪ʰɐ̞́.jó̞ᵝˑ.ɾ̪ʲì wò̞ᵝ í.jýˑ.ɾ̪è̞]
SOME-NEGATIONAL-WORD SOMEETHING ADJECTIVE.NOUN.ACCUSATIVE speak.SOME-INFLECTION
おておでの すず より しほざけを すへ、
Otyode no suzu yori shōzakyo sue,
[ó̞ᵝ.t̪ʰʲó̞ᵝˑ.d̪è̞ n̪ò̞ᵝ s̪ʉ́ᵝˑ.z̪ʉ̀ᵝ jó̞ᵝ.ɾ̪ʲì ɕʰó̞ᵝː.z̪ɐ̞́ˑ.c͡çʰi̯ò̞̞ᵝ s̪ʉ́ᵝ.wè̞]
SOMETHING RELATIONAL not-a-bell-but-close.CASE-MARKER ADJECTIVE.NOUN.ACCUSATIVE verb.SOME-INFLECTION
「くっく」とう をたへさく なつ こうれ...
Kukku to wotaesaku natsu kore...
[kʰʉ́k.kʰʉ̀ᵝ t̪ʰò̞ wò̞ᵝ.t̪ʰɐ̞́.è̞.s̪ɐ̞́ˑ.kʰ ʉ̀ᵝ n̪ɐ̞́ˑ t̪͡s̪ʰʲỳᵝ kʰó̞ᵝˑ.ɾ̪è̞]
SOME-ONOMATOPOEIA.QUOTATIVE VERB.SOME-INFLECTION.SOME-SUFFIX summer MAYBE-A-VERB
Mukutsu kukkute wotae tobe,
[mʉ̀ᵝ.kʰʉ́ˑ.t̪͡s̪ʰʲỳᵝ kʰʉ́k.kʰʉ́ˑ.t̪ʰè̞ wò̞ᵝ.t̪ʰɐ̞́ˑ.è̞ t̪ʰó̞ᵝˑ.bè̞]
SOMETHING SOMETHING.DEFINITE VERB.SOME-INFLECTION VERB.SOME-INFLECTION
ぜひ むそう よたよるゐを いふれ、
Zei muso yotayori wo iyure,
[z̪ê̞ː mʉ́ˑ.s̪ò̞ᵝ jò.t̪ʰɐ̞́.jó̞ᵝˑ.ɾ̪ʲì wò̞ᵝ í.jýˑ.ɾ̪è̞]
SOME-NEGATIONAL-WORD SOMEETHING ADJECTIVE.NOUN.ACCUSATIVE speak.SOME-INFLECTION
おておでの すず より しほざけを すへ、
Otyode no suzu yori shōzakyo sue,
[ó̞ᵝ.t̪ʰʲó̞ᵝˑ.d̪è̞ n̪ò̞ᵝ s̪ʉ́ᵝˑ.z̪ʉ̀ᵝ jó̞ᵝ.ɾ̪ʲì ɕʰó̞ᵝː.z̪ɐ̞́ˑ.c͡çʰi̯ò̞̞ᵝ s̪ʉ́ᵝ.wè̞]
SOMETHING RELATIONAL not-a-bell-but-close.CASE-MARKER ADJECTIVE.NOUN.ACCUSATIVE verb.SOME-INFLECTION
「くっく」とう をたへさく なつ こうれ...
Kukku to wotaesaku natsu kore...
[kʰʉ́k.kʰʉ̀ᵝ t̪ʰò̞ wò̞ᵝ.t̪ʰɐ̞́.è̞.s̪ɐ̞́ˑ.kʰ ʉ̀ᵝ n̪ɐ̞́ˑ t̪͡s̪ʰʲỳᵝ kʰó̞ᵝˑ.ɾ̪è̞]
SOME-ONOMATOPOEIA.QUOTATIVE VERB.SOME-INFLECTION.SOME-SUFFIX summer MAYBE-A-VERB
