I'll offer my take on a few of your questions, Paul ... I've de-bolded your bold and bolded my comments:

While that my soul repairs to her devotion,
Here I entomb my flesh, that it betimes
May take acquaintance of this heap of dust,
To which the blast of Death's incessant motion,
Fed with the exhalation of our crimes,
Drives all at last. Therefore I gladly trust

So far, no problem: soul is feminine (her), flesh is neuter (it), Death of indeterminate gender

My body to this school, that it may learn
To spell his elements, and find his birth
Written in dusty heraldry and lines;
Which dissolution sure doth best discern,
Comparing dust with dust and earth with earth.
These laugh at jet and marble, put for signs,

Here, body is, like flesh in first stanza, is neuter; but does it become masculine in line 2 (“his elements”), or does “his” refer back to Death? (Hard to see how this second reading would work, but why the shift from neuter to masculine?)

"his elements" refers, in my mind, to Death - which was not 'neuter' in the first stanza but rather indeterminate, with no pronoun yet referring back to Death until here, and now it's established as masculine.


Is “dissolution” the subject or the object of the verb “discern”? still pondering that one, but I lean toward "subject" in a transcendental kind of way, where the implied subject of 'discern' is really a myriad of forces ... To me, "dissolution sure" here means "certain/inevitable dissolution" and it's that 'fact' which does the discerning - and allows us to fathom the discerning of what to make of the realities of dust and earth and the fate of life

What is the referent of “These”: the body’s elements? Dust and earth? Dissolution and the body?
For me, "These" seem to be dust and earth

To sever the good fellowship of dust,
And spoil the meeting: what shall point out them,
When they shall bow, and kneel, and fall down flat
To kiss those heaps which now they have in trust?
Dear flesh, while I do pray, learn here thy stem
And true descent, that, when thou shalt grow fat,

Here, “them” in line two apparently refers to the headstones, but grammatically one would expect it to have the same referent as “These” in the last line of the preceding stanza.
Not sure why grammar would make it need to be same referent as for "These" - I agree, for now, that it refers to headstones.

And wanton in thy cravings, thou mayst know
That flesh is but the glass which holds the dust
That measures all our time; which also shall
Be crumbled into dust. Mark here below
How tame these ashes are, how free from lust,
That thou mayst fit thyself against thy fall.

“Thou mayst know / that flesh . . .” But “Thou” refers to flesh, so the sense is “Flesh, thou mayst know that flesh . . .”—it’s reflexive, circular.
For me, not quite circular. I think he's speaking to his particular flesh and wishing it to learn the message of all flesh, of flesh as a concept, ... To me, the poet has gone to philosophical jelly of sorts upon a lingering deliberation of "ashes to ashes, dust to dust" ... and this poem has resulted from it ... To me, the "while I do pray" in penultimate stanza, alludes back to the first stanza's "While that my soul repairs to her devotion,..." His soul is inside the church praying for salvation, while his flesh is lingering here in the church graveyard reckoning with the meaning of the Biblical lines "dust to dust" (and hence the plethora of 'dusty' references - which I was going to comment on but Woskin already had (the movement from linking dust and trust toward linking dust and lust) ... And in that sense (moving on to your last question...

Speaking of reflexivity, the reflexive use of “fit” (“fit thyself”) is unusual: does it mean to adapt oneself? To proportion oneself? To prepare oneself? The sense requires some pondering to discern.

I read this as meaning "to prepare oneself" ... There's almost a pantheism here, it seems, a notion of soul in everything including dust ... The poet beseeches his flesh to see lessons in how to leave earthly life in the "tame"ness of ashes/dust ... wishing to find succor, it seems, in the idea of tameness/calmness that will both compensate for the loss of lust for life and also make lust seem very 'passé' (so to speak) ... thus to let go of lust, to see it as that which will be left behind ... and so not to anguish at its loss ... Ending the poem with "thy fall" (and the only slant rhyme - the second noteworthy aspect of rhyme in the poem, the first being the re-use of 'dust' 3 times) would seem to evoke Satan's fall as well ... and there would seem, by contrast, to be a 'lusty' one, who anguished and belabored his fall and wreaked much havoc from it ... So perhaps that a contrastive invocation here, that his own flesh cede more gracefully into its fall...

my 2 c's ...