"... His entreaties which are hearkened/hearkened unto by God"

Solution 1:

Hearken is usually a prepositional verb in that it most frequently appears (appeared) in a construction with an oblique object (one contained in a prepositional phrase) when there was an object present.

The HANSARD corpus (British Parliament) has three examples in the passive.

I can only hope that the words of the Foreign Secretary will be hearkened to by nations beyond the seas (1936)

Members might ask themselves how that plea has been hearkened to by the Tories of Northern Ireland who comprise about two-thirds of the people there (1920)

I hope that my plea will be hearkened to by the noble Lords opposite, and that nothing will be done this afternoon to delay getting this Bill on to the Statute Book (1966)

COHA (Corpus of Historical American English) yielded one example in the passive:

he was scarcely hearkened to at all by his contemporaries, who looked upon him as merely an ingenious sort of madman (The Works of Edgar Allan Poe — Volume 4, 1855)

The EEBO corpus (Early English Books Online) has quite a few uses in the passive with unto or to. A sample:

Wherfore that you may as a fresh be put in minde hereof, and the exhortations of the apostles hearkened unto by you, i thinke fit in this place to set before you some of them (Proctor, Thomas, fl. 1621.)

it were too presumptuous a thought in me to expect, that any advise of mine should be hearkened unto by you who have so many learned and renowned doctors to consult upon all occasions (Gatford, Lionel, d. 1665.)

their advice scarse at all hearkened unto by the king, but other counsels of unknowne persons preferred before them (May, Thomas, 1595-1650.)

a meer forgery, yet gladly hearkened unto by those that desired to be rid of them (Spottiswood, John, 1565-1639. | Duppa, Brian, 1588-1662.)

a motion had been made a little before, for appointing a commissioner or Deputie in the Kingdome, which was hearkened unto by the king as that which would ease him of many vexations (Spottiswood, John, 1565-1639. | Duppa, Brian, 1588-1662.)

that their arguments are not hearkened vnto but by people of a weake braine (1629, Sarpi, Paolo, 1552-1623. | Brent, Nathaniel, Sir, 1573?-1652.)

let it be seriously hearkened to by all the ministers of christ (Brinsley, John, 1600-1665.)

this motion was not hearkened to by men grown fierce (Clarke, Samuel, 1599-1682. Gun-powder treason. 1671)

the affairs of the league seemed not to be hearkened to by him with the same inclination wherewith his predecessors had imbraced them (1678, Davila, Arrigo Caterino, 1576-1631. | Aylesbury, William, 1615-1656. | Cotterell, Charles, Sir, d. 1701. | L'Estrange, Roger, Sir, 1616-1704.)

about two years before this there appear'd in cromwel's time a prophetess, much fam'd for her dreams and visions, and hearkened to by many (Behemoth, or, An epitome of the civil wars of England, from 1640 to 1660 by Thomas Hobbes)

Thereunto was apparently also a choice:

it hath had this blissing to thousands and ten thousand thousands that haue hearkened thereunto (Babington, Gervase, 1550-1610.)

the Bishoppe promised his best diligence, and accordingly after his returne, laboured therein with king henry, who most gladly hearkened thereunto (Speed, John, 1552?-1629.)

who hath considered of his word, and hearkened thereunto? (1638)

A few examples exist with hearken taking an object, but I couldn't find any examples in the passive without a preposition.

moses excuseth himselfe unto the lord, saying, they would not beleave him nor hearken him, alledging, that the lord had not appeared unto him (Goodwin, John, 1594?-1665.)

he shall crie to Iesus christ at his last daie, and scarcely woll he hearken him (1687)

sim sure: let vs hearken them ( Udall, Nicholas, 1505-1556.)

i see now from afarre what thou purposest, algates i desire yet to hearken it of thee more plainly (1687)

thou shalt holly with all thy wit Doe thine entent to hearken it: yes sir (1687)

So in answer to your question, it seems that both the use with and without a preposition are (were) possible, the prepositional version being apparently the more common.

Solution 2:

This is a simple case of distinguishing between transitive and intransitive verbs.

Used transitively, hearken warrants a direct object, and that's how your first version reads (in the passive voice, of course.)

Here's how M-W defines hearken transitively:

archaic : to give heed to : HEAR

The active voice version would read:

His entreaties, which God hearkens, would always prevail.

But the verb hearken (like most other verbs) could be used intransitively as well, and that's where the fancy-sounding preposition unto (which is actually a stylized version of the modest to) comes into play— because intransitive verbs, by definition, don't take a direct object.

And that's why the active voice of your second version would read:

His entreaties, which God hearkens unto/to, would always prevail.

But as you have mentioned in the question itself— and as AHD concurs— this latter version has a rather formal and archaic air.

And as regards who is "more" correct— you or your friend— the answer is neither, because it is simply a case of using a verb in its two different avatars.

Sentence 2 seems heavier and less successful, perhaps because of the juxtaposition of two prepositions (unto by).

I take this misgiving with a pinch of salt: it is par for the course in English to see such constructions. A phrasal verb (Verb+Preposition combo), for instance, when passivized would almost always take after it another preposition.