Modern convention on this cello passage

[John Ruggero]

Thanks for the great explanation, Neera!

[NeeraWM]

You are most welcome!

Here are two possible options:
(1)

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(2)

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The first one is hyper-clear, with complete string indicators and harmonic circles.
The second one—which I would expect coming from a non-string-player composer—only states the minimum necessary to avoid any misunderstanding. 0+circle = open string + harmonic, with one and only one option to play that correctly. 'III' under the D-A is unmistakable: 4th position, G-D strings.
'0' above D-C may appear misleading but it is again super-clear because there is no middle-C open string on cello so it must be the D.
In this last case, a 'II' under D-C may have not been enough because the middle-C is available in the D string in the previous position.

[John Ruggero]

One question, Neera. Were I the composer and this not an educational work or edition of a standard work with editorial fingering and bowing, I'd only put in the one harmonic indication and assume that the rest was obvious to an experienced cellist. Isn't that the normal way to handle this when nothing special is being asked for?

[NeeraWM]

Yes, John.
The harmonic would be needed because the fourth is not a friendly interval on the cello.
What would prompt players to play on the middle strings would be the PP.