The Nyāya-Vaiśeṣika texts don't mention the specific numerical value of parārdha, what values you probably saw in the Praśastapāda's Padārthadharmasaṅgraha (PDS) has been added by the translator, and isn't there in the original text or its commentaries, as you already figured out.
Also, an important point to note is that, the parārdha used by Praśastapāda and the commentators on his work PDS is not the same as that used by Bhagavata Purāṇa, which refers to half-life of Brahmā. And Viṣṇu-Purāṇa is not the right source to know parārdha in the Nyāya-Vaiśeṣika context.
As we see in PDS, after one, the numerical qualities run from 2 to a large but finite number parārdha. The number parārdha is mentioned in many texts as the highest decimal place name.
The precise value of parārdha varies: in the Taittirīya Saṁhitā (188.8.131.52, 184.108.40.206) and the Maitrāyanī Saṁhitā (2.8.14), it is given as 10^ (12), while the Kāṭhaka Saṁhitā records both 10^12 (17.10) and 10^13 (39.6). Among the mathematicians and the mathematics treatises such as Līlāvatī by Bhāskara II, it is always 10^(17) i.e. a hundred quadrillion (which you read).
There are names for higher decimal powers in Buddhist and Jaina texts (for e.g. Abhidharmakośa 3.93-94 names powers up to 10^ 59). Only the Nyāya-Vaiśeṣika take parārdha to be the highest number, and not merely the highest named placed value.
It's important to understand the notion of many, in order to grasp parārdha in the Nyāya-Vaiśeṣika context, Śrīdhara is said to have argued that many is itself a number, distinct from any number in the cardinal series. This is based on his view presented by Śaṅkara Miśra (1923:179)
‘Since in the case of a forest or an army, there is no definite combinatory cognition [i.e. counting up of the number of trees or men],a mere many-ness comes into being, but not the number a hundred or a thousand’ – this is the view of the teacher Srīdhara.
According to Śrīdhara, numbers are created by mental acts of counting, but the uncounted army or forest has no definite no. of men or trees. Thereby, Śrīdhara's view is that, in such a case, is of an indefinite act of counting procedures in the objects the indefinite number, many. This problems is due to clear delineation of uncounted collection of objects, which might, as in these cases, be a perceptible aggregate or it might be picked out under a description, for instance 'planets in solar system'. Thus, there seems to be inconsistency with common-sense intuition that the collection has some definite if unknown number, and the Nyāya-Vaiśeṣika thesis that number is the result of a mental act of counting up the objects in the collection.
Udayana (1956:179 & 458-459), on the other hand, insists on the validity of common sense, that a doubt about the number of men in the army only arises when one thinks of it as having a definite but unknown number. Furthermore, if many is really a number, then we would not be able to judge one group of many from the other and say which one is larger or smaller. Thus, Udayana states on the basis of his argument, a definite or precise mental act of counting is both the cause and the manifestor of the number whereas an indefinite or imprecise mental counting is the cause but not the manifestor of a number.
Uddyotakara (1985:211) links the distinct many with processes of increase while Śaṅkara Miśra (1923:180) goes ahead and points that many denotes neither a particular number in the cardinal series nor the series in totality, but rather a property (of being large in no) that co-exists with the definite number the object possesses.
Actually, there is no room for the idea of maximal finite number such as parārdha if one thinks of the number series as generated by recursive application of the successor function, unless in the case of Bhāsvarjña who attempts to construct such a number series.
However, within a conception of numbers as qualities of substances, indeed, it seems that there has to be a largest number, if the number of things in the cosmos is finite. But that largest such number (parārdha) need not be definite, and that's what the case is in PDS and it's commentaries.
References & Further Reading
Ganeri, J. (2001). Objectivity and Proof in a Classical Indian Theory of Number. Synthese (Dordrecht), 129(3), 413–437. https://doi.org/10.1023/A:1013144411940
Śrīdhara: Jha, Durgadhara (Ed.) (1977), Praśastapāda with the commentary Nyāyakandalī by Śrīdhara Bhaṭṭa (D. Jha, Trans. in Hindi). Ganganatha Jha Granthamala Vol. 1.(pp. 267–214). Sampurnanand Sanskrit Vishvavidyalaya
Śaṅkara Miśra: Sastri, Dundhiraja (Ed.) (1923), Vaiśeṣikadarśana with Praśastapāda's Padārthadharmasaṅgraha with Śaṅkara Miśra's Upaskāra. Kashi Sanskrit Series 3 (pp. 173–180).Chaukhamba Sanskrit Series Office
Udayana: Vedantirtha, N.C.(Ed.) (1956) Kiraṇāvalī with Vardhamāna's Prakāśa and Vādīndra's Rasasāra. Bibliotheca Indica no. 200, fasc. 4. (pp. 441-462). The Asiatic Society
Gautama: Nyāyatarkatīrtha, T. & Tarkatīrtha, A. (Eds.) (1985), Nyāyasūtra with Vātsyāyana Bhāṣya, Uddyotakara's Vārttika, Vācaspati Miśra's Tātparyaṭīkā and Viśvanātha's Vr̥tti. Calcutta Sanskrit Series no. 18-19 (2nd ed). Munshiram Manoharlal