There's a simple trick to prove that Hindi or any IA language is as old as Tamil, Telugu or Kannada.
The hint is hidden in Phonology.
It's a known fact that standard register of Tamil is very much based on medieval Tamil. Same applies to Kannada.
Indo-Aryan languages except Sinhala, Dhivehi rarely experience a diglossia where written form is based on medieval grammatical forms.
Let's discuss each and every point one by one.
1) ऐ or अय could become ए using Prakrit rules.
करोति (Sanskrit) »
करइ (Prakrit) » करे (Hindi)
देवालय, शिवालय » देवाले, शिवाले (Temple)
Now come to Tamil.
கிடைக்கும் » கெடெக்கும் (Available)
किडैक्कुम् (Formal) » कॆडॆक्कुम् (Informal)
வரைவாள் -> வரெவா (She draws)
वरैवाळ् (Formal) -> वरॆवा (Informal)
2) अय, आय could become ए likewise
पाइलो (Medieval Bangla) » पेलो (He got) (Modern Bangla)
Again come to Tamil.
வருவாய் » வருவே (You come)
वरुवाय् » वरुवे
போனாய் » போனே (You go)
पोनाय् » पोने
Further, there are even more phonetic corruptions in Modern Tamil and Malayalam from Middle Tamil which could have preserved better in their pristine originality in IA languages.
த்த » ச்ச (त्त » च्च)
ந்த » ஞ்ச (न्द » ञ्ज)
Considering the above corruptions, I think Awadhi is more closer to Apabhramsha (the counterpart of Middle Tamil).
Next time some South Indian rants about classical status of their own language, consider showing this as proof and conclude with this saying “उलटा चोर कोतवाल को डाँटे!”