Manu Leumann's Lateinische Laut- und Formenlehre (Munich 1977) groups the contraction of -āvis- to -ās- in forms like amāstī and amāssem together with the contraction of -āver- to -ār- in forms like amāram and amāro. Leumann says that "Bei Plautus sind noch die Kurzformen seltener als die Vollformen" ("in Plautus, the short forms are still rarer than the full forms") (§438.II.B, p. 599).
That remark is only for first-conjugation perfect forms of the āvī type; Leumann discusses other types of perfects, and other specific words, in other parts of that section. For example, he says that Plautus prefers the short forms of audīre.
For further details, Leumann says to consult "Stolz, KZ 38, 429", which Alex B has identified in a comment as "Über Angeblichen Wandel Von Lat. āνĕ Zu ā." Zeitschrift für Vergleichende Sprachforschung auf dem Gebiete der Indogermanischen Sprachen 38, no. 3 (1905)". I'm still processing what Stolz says, but the main thing that's relevant to your question is some figures and some suggestions about the development of the forms in -ās- and -ār-. Stolz says that in Plautus, forms in -āverim -āveram -āverō are seven times as common as forms in -ārim -āram -ārō, forms in -āvistī are a little less than twice as common as forms in āstī, and forms in -āvērunt are more common than forms in -ārunt; but forms in -āvisse(m) are not quite as common as those in -āsse(m) (citing Brock 140, 134, 143, 124) (pp. 429-430). Based on frequency of forms and phonetic considerations, Stolz suggests that the replacement of -āvis-/-āver- with -ās-/-ār- developed by analogy with the loss of -v- in perfect forms of -ēvi and -īvi verbs (p. 429). Stolz doesn't think that -āvĕ- > -ā- was a usual sound change in Latin, because we can find -āvĕ- in cadāver and papāver (p. 426).
In "A Note on Servivisti (Petr. 57.4)" (1998), Brent Vine quotes Leumann's statement that short forms of the perfect (in general, not of -āvī-perfects specifically) "gehören seit Plautus der Umgangssprache an" (are heard from the Vulgar Latin of Plautus onward) and goes on to discuss two passages that Leumann cites to support this: one is the Quintilian passage that you have already mentioned (1.6.17), and the other is Cicero Orat. 155-62. Vine says that the context of these passages is the argument between the "anomalist" and "analogist" schools of grammar.
In Orator 155-62, Cicero says that the full forms novisse and iudicavisse are the ones that are thought of as "correct", but the short forms nosse and iudicasse are the ones that are usual in speech. Wikipedia says that Orator was written in 46 B.C. In fact, Cicero does seem to have used the form "iudicavisse" occasionally in his earlier works (e.g. In Verrem, which Wikipedia says is from 70 BC).
In a footnote (8), Vine says "I hope to treat elsewhere the pedagogical implications of the fact that we routinely teach our beginning students forms like audivisti (and similarly audivisse, audivissem etc.) which are in fact largely unattested."
As the title indicates, Vine's article is mostly about a particular occurrence of "servisti". Vine says that servivisti is "the sole uncontracted -vis-perfect form in the entire Satyricon (including 2 sg. pl. perf. -visti/-vistis, perf. act. infin. -visse, and plupf. subj. -vissem, -visses, etc.)" (p. 543). Wikipedia says that there is now a consensus that the Satyricon was written in the time period of Nero (1st century AD).