No, those two forms have no rhyme structure as such, but alliteration is encouraged. Love your poem, by the way, Aine-that's a keeper.

In keeping with the steadily increasing trickiness, the next form is Ljothaháttr, the meter of chants. The meter is made up of pairs of lines, each with two stressed syllables and bound by alliteration, followed by a third line called "the full line" which has its own alliteration and either 2 or 3 stressed syllables. Normally two segments of three lines make up a stanza.
From Havamal:

Byrthi betri
berrat mathr brautu at
en sé mannvit mikit;
vegnest verra
vegra hann velli at
en sé ofdrykkja ols.

(Burden better
bears none abroad with him
than a cool discretion;
with worser food
will fare you never
than a big load of beer.)

And this is my try at it:

Love lingers
When limbs are limber
Tender is a young love's timbre
When gold is grey
And glory gone
Lib'ral love fades ever dimmer.


And now the other version of Ljothaháttr,
Galdralag "magic spell meter" uses a fourth line which echoes and varies the third line of the stanza.

From the Eggjum grave stone, Sogn, Noway ca. 700 C.E.:

Hverr of kom Heráss á
hí á land gotna?
Fiskr ór fjanda vim svimandi,
fogl á fjanda lith galandi.

(As whom came War-god
hither to the land of men?
A fish from the torrent of enemies swimming,
A bird against troop of enemies screaming.)

From my head, 2005:
(to Vinland)

They flee the eager priest
adversity unceasing
To verdant southern reaches
To virgin southern beaches.
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