I have not studied the Rubaiyat of Omar Khayyam so my comments can only be brief and tentative. I suspect Hiram has so maybe he will have more comment.

But if his primary parallel to Epicurus is "his attack on the theistic or conventional judgments and his praise of simple pleasures" then we would want to explore his views on physics and epistemology as those are critical to any conclusions about ethics.

Ecclesiastes in the Bible is also deeply pessimistic and shows some Epicurean influence (the Epicureans were a major school in Antioch and in the vicinity of Judea when it was written), but it can't ultimately be reconciled with E for its claim that all wisdom begins with fear of God.

My new avatar is Omar Khayyam, painting by Adelaide Hanscom (c. 1910).

The following is from Wikipedia:

"FitzGerald emphasized the religious skepticism he found in Omar Khayyam.^[10] In his preface to the Rubáiyát, he describes Omar's philosophy as Epicurean and claims that Omar was "hated and dreaded by the Sufis,..."

Quote

The extreme popularity of FitzGerald's work led to a prolonged debate on the correct interpretation of the philosophy behind the poems. FitzGerald emphasized the religious skepticism he found in Omar Khayyam.^[10] In his preface to the Rubáiyát, he describes Omar's philosophy as Epicurean and claims that Omar was "hated and dreaded by the Sufis, whose practice he ridiculed and whose faith amounts to little more than his own when stripped of the Mysticism and formal recognition of Islamism under which Omar would not hide".^[11] Richard Nelson Frye also emphasizes that Khayyam was despised by a number of prominent contemporary Sufis. These include figures such as Shams Tabrizi, Najm al-Din Daya, Al-Ghazali, and Attar, who "viewed Khayyam not as a fellow-mystic, but a free-thinking scientist".^{[7]: 663–664} The skeptic interpretation is supported by the medieval historian Al-Qifti (ca. 1172–1248), who in his The History of Learned Men reports that Omar's poems were only outwardly in the Sufi style but were written with an anti-religious agenda. He also mentions that Khayyam was indicted for impiety and went on a pilgrimage to avoid punishment.^[12]

The Rubaiyat of Omar Khayyam [excerpt]

Edward Fitzgerald

1

Wake! For the Sun, who scattered into flight

The Stars before him from the Field of Night,

Drives Night along with them from Heav'n and strikes

The Sultán's Turret with a Shaft of Light.

2

Before the phantom of False morning died,

Methought a Voice within the Tavern cried,

"When all the Temple is prepared within,

Why nods the drowsy Worshiper outside?"

3

And, as the Cock crew, those who stood before

The Tavern shouted--"Open, then, the Door!

You know how little while we have to stay,

And, once departed, may return no more."

12

A Book of Verses underneath the Bough,

A Jug of Wine, a Loaf of Bread--and Thou

Beside me singing in the Wilderness

Oh, Wilderness were Paradise enow!

13

Some for the Glories of This World; and some

Sigh for the Prophet's Paradise to come;

Ah, take the Cash, and let the Credit go,

Nor heed the rumble of a distant Drum!

14

Look to the blowing Rose about us--"Lo,

Laughing," she says, "into the world I blow,

At once the silken tassel of my Purse

Tear, and its Treasure on the Garden throw."

15

And those who husbanded the Golden Grain,

And those who flung it to the winds like Rain,

Alike to no such aureate Earth are turned

As, buried once, Men want dug up again.

19

I sometimes think that never blows so red

The Rose as where some buried Caesar bled;

That every Hyacinth the Garden wears

Dropped in her Lap from some once lovely Head.

20

And this reviving Herb whose tender Green

Fledges the River-Lip on which we lean--

Ah, lean upon it lightly! for who knows

From what once lovely Lip it springs unseen!

21

Ah, my Belovéd, fill the Cup that clears

Today of past Regrets and future Fears:

Tomorrow!--Why, Tomorrow I may be

Myself with Yesterday's Sev'n thousand Years.

22

For some we loved, the loveliest and the best

That from his Vintage rolling Time hath pressed,

Have drunk their Cup a Round or two before,

And one by one crept silently to rest.

23

And we, that now make merry in the Room

They left, and Summer dresses in new bloom,

Ourselves must we beneath the Couch of Earth

Descend--ourselves to make a Couch--for whom?

24

Ah, make the most of what we yet may spend,

Before we too into the Dust descend;

Dust into Dust, and under Dust to lie,

Sans Wine, sans Song, sans Singer, and--sans End!

71

The Moving Finger writes, and, having writ,

Moves on; nor all your Piety nor Wit

Shall lure it back to cancel half a Line,

Nor all your Tears wash out a Word of it.

72

And that inverted Bowl they call the Sky,

Whereunder crawling cooped we live and die,

Lift not your hands to It for help--for It

As impotently moves as you or I.

The Rubaiyat of Omar Khayyam [excerpt] by Edward Fitzgerald - Poems | poets.org

"A book of verses underneath the bough,
a jug of wine, a loaf of bread--and thou
beside me singing in the wilderness--

Oh, wilderness were paradise enow!"

This was a treasured statement of our philosophy when my wife and I lived a more simple life (for 15 years) in what I called our "widly garden'": growing vegetables in the kitchen garden, cutting and splitting wood for winter, planting fruit trees, gathering blackberries and wild cherries -- and my wife's homemade wine. Doesn't seem pessimistic at all to me.

But, re the Khayyam quote, I always thought Epicurus might have quipped: "Why are you in a wilderness? Are their no civilized gardens around?"