How would you eloquently say "doing something for the umpteenth/nth/n-tieth time"?

I don't think one word will do what you want. How about "She reloaded the gun fluidly and repeatedly"

Fluidly means moving like a fluid, in a smooth, continuous manner. Synonyms for fluid, from Collins English Dictionary are:

flowing, easy, natural, smooth, elegant, graceful, fluent, effortless, feline, sinuous

repeatedly is defined here as:

over and over again; constantly

Another phrase the OP might use is:

Yet once again, she reloaded the gun.

To my surprise, the search for yet once again found that it it is from a poem From Lands Afar written for the Salvation Army's International Congress in 1914. (Author, Albert Orsborn).

Edit in Response to Comment by Dave_Thompson_085

See Google Books Yet once again for quotes from Shakespeare, Milton, Wordsworth, Dickens, Southey, and many, many other writers. Just one example (Wordsworth) from dozens, perhaps hundreds:

Yet once again do I behold the forms Of these huge mountains, and yet once again, Standing beneath these elms, I hear thy voice, Beloved Derwent, that peculiar voice Heard in the stillness of the evening air, Half-heard and half-created.

umpteenth, adjective, informal –TFD

Relatively large but unspecified in number: umpteen reasons; umpteen guests.

Doing something for the umpteenth time.

"umpteen," meaning a large but unspecified number or "umpteenth," meaning the latest in a long series would work:

"She reloaded the gun umpteen times."

or

"She was reloading the gun for the umpteenth time."

She was reloading the gun again.

Is this usage in the character's head/internal dialogue? Simply 'again' would indicate that it is a repetitive action.

In business terminology (and math and statistics), there is the idea of marginal units, which means the next unit, as in marginal cost, marginal profit, etc. However it does not flow well with the context you have proposed.

Matilda hefted the handgun. After years of work she knew, simply by the weight and balance of the thing, how many bullets were left. Three. She’d need more. Of course.

She scanned the horizon as she reloaded. Casual, autonomic, an act of physical memory. As familiar and easy as brushing her hair. No effort needed. The satisfying sound of gunmetal clipping into place.

Click the magazine latch off. Dust on the Old Road, about 5 miles south.

Flick the cylinder open. Thumb it round. Shake out the spent cartridges. One movement. A truck- dust's too thick for a sedan.

Snick three bullets into the cylinder. Flick cylinder closed. Spin. One movement. In a hurry. Big hurry.

Matilda snuggled down behind the rocks. Shaded her eyes, watched as the dark shape of the vehicle formed out of the heat shimmer. Rehearsed the hit.