To reply to your "Devil's advocate" comment:
The hypothesized (P)IE root form is based on the wrong assumption that the Sanskrit (uvasa-) and Greek (Eos) forms are closest to the original. This runs into problems because 1) replacing 'oldest' by 'closest to the original' is an oversimplification and 2) the assumed root form fails to explain the consonantal clusters in Proto-Germanic and the rhotacized forms in Italic because of the general trend towards avoiding these clusters throughout the evolution of IE languages.
I really don't understand the nature of this objection. The root reconstructions are not based a methodology of treating the oldest languages as the ones closest to the original. They are based on establishing sound correpondences, determining patterns of complementary distribution, and reconstructing systematic phonemic sets for each language. This is a methodology that has been used for 150 years and is still regarded as the best means of assessing genetic relationship between languages. Do you mean to say that the reconstructions of *awes, *aus did not follow this methodology? And regardless of which language is "closest to the original", these are well-established cognates. My point is that the Indo-European and Semitic names are based on unrelated roots in each respective language.
I also don't follow the second comment. Do you have a source for the claim that the reduction of a suffix like "ter" (with a weak vowel) to "tr" is actually avoided in Indo-European? My impression is the exact opposite; it is one of the most natural reductions I can imagine (and crosslinguistically, suffixes tend to be reduced). There are countless other examples of this reduction in Indo-European languages: *apo-tero "in a direction away from behind" (whence Sanskrit apataram, Greek apóteró "farther distant", Proto-Germanic *aftaro, *aftra < Gothic aftaro "from the back", aftra "back, again", and English after, aft), *en-tero "inward, in a direction inside" (whence Hittite anturias "inner", Sanskrit antara "internal", antrá "entrails", Greek enteron "entrails", Armenian enderk "entrails", Albanian nder "in between", Latin enter, inter "among, between", interus, intrá "internal", intestinus "entrails", Oscan anter "between, among," Entrai "Interae", Gaulish ínter "between", Cornish ynter, yntre "between", Breton entre "between", Old High German untar "between, under", Old Norse ithrar "entrails", ithre, innre "inner"), *kwo-tero "which between others" (whence Sanskrit katara, Greek poteros, Umbrian putres-, Gothic hwathar, Old English whaether, Lithuanian katras), etc. Compare also the word for "mother" (*mátér, whence Latin mátér and Greek méter) and the derived word for "womb" (*matr-, whence Latin mátríx and Greek métra), or the word for "husband's brother's wife" (*yenetér, whence Phrygian ianatera, Greek enater, enatri, Latin janitrícés, Latvian jentere, Old Church Slavonic jetry). Roots also had regular ablaut zero-grade forms in Proto-Indo-European, e.g. nominative *patér "father" and genitive *patros "father's".
As for the s -> r shift in Latin (with a following vowel or nasal), this is actually very typical in Latin and Germanic, e.g. *aus "ear" in Greek ous, Latin auris, Gothic auso, Old High German óra, Old English eare, Lithuanian ausis, *ayos "metal, ore" in Sanskrit ayas, Latin aes, aeris, Gothic aiz, Old English ár "ore", *dhés "religious, holy" in Sanskrit dhisnya "devout, godly", Oscan fiisnam "shrine", Latin fésiae, fériae "holidays, festivals", *eis "passion, madness, fierceness" in Greek oistros "frenzy, madness", Latin eira, íra "anger", Old Norse eisa "storm along", *esus "master, owner" in Gaulish PN Esus, Latin esa, era "mistress, lady", erus "master, lord", *es- "to be" in Sanskrit asti "he is", Greek esti "he is", Latin est, "he is", preterite erat, future eró, Old Norse ert "you are", Old English eart, Old Church Slavonic esti, *ghais "to stick to" in Latin haereó, haesí "to hang or hold fast", *gheiso "stick, dart" in Greek khaios, Latin gaesum, Gothic PN Gaisu-, Old High German gér, Old Norse geirr, *ghzhies, *ghzhies-tero "yesterday" in Greek khthes, ekhthes, Latin here, hesternus "previous time", Gothic giestran, Old High German gesteren, *kwes "to sigh, lament" in Sanskit svasiti, Latin questus, queror, Old High German hwósan "gasp", *leis "track, furrow" in Latin líra, Old High German leisa, lesa "wrinkle", léren "teach", Gothic laists, *nas "nose" in Sanskit nasa, Latin násum, náris, nárium "nose, nostril", *os, *os-enos "ash tree" in Latin ornus, Illryian PN Osones, Old Norse askr, Lithuanian uosis, Serbian jasen, *os "mouth" in Sanskrit ás-, Latin ós, óris "mouth, face", Old Irish ór, Old Church Slavonic usta, *peis, *speis "blow, breathe" in Latin spíró, Old Norse físa "blow, fart", Old Church Slavonic piskati "whistle", Albanian piskat "scream", *weis "sprout, grow" in Latin víreó "become green", Old Norse vísir "germ, sprout, scion", Old English wíse "shoot, scion", Lithuanian veisti, veislus "fertile", Latvian vaisla "scion, brood", *weiso "poison, slime" in Sanskrit vísa, Avestan visha, Greek [w]ios, Latin vírus, Old Norse veisa "swamp", Old English wáse "slime, ooze", *wes, *westi "to dress, wear" in Hittite wash-, Sanskrit vaste, Greek hessai, Latin vestis "clothing", Gothic wasjan, wasti "dress", Old High German werian, Old English werian, Tocharian B wastsi "dress", *yewos "law" in Latin jús "statute", jústus "justice", júró "to swear, vow", etc. The rhoticization can frequently found in Latin in noun declensions and verbal conjugations of roots with /s/.
It must be borne in mind that in the case of *awes, *aus, we are dealing with two different suffixes in the derived forms, *aus-ós and *aus-t(e)ro. The former word is attested in such forms as Greek éós, auós "aurora" (from *auhós, cf. intravocalic s -> h in Greek), Latin auróra (also cf. Latin aurum "gold" and Sabellic ausom "gold"), Welsh gwawr "aurora", Old Lithianian ausas, etc. The latter occurs in Latin auster, austrális, Old High German ostar, Old Norse austr, Latvian austra "daybreak", Old Church Slavonic ustra, etc. The rhoticization occurs with the suffixation with -ós not -t(e)ro.
