I don't want to hear arguments over the pnounciations of 'V' and 'C' and 'Æ' and the like. No-one can prove it, just pronounce it however you want and leave it at that.
Sorry, I haven't read the whole thread, but I just have to contradict this. You can prove both the velar stop and the diphthong for the classical period, unless you don't accept loans into Germanic as proof.
The case in point is that caesar was borrowed into Old High German as kaisar. Had there been a monophthong, it would have been kiasar and we'd say Kieser instead of Kaiser in New High German.
Now if that's not a proof, nothing is for the purposes of historical linguistics...
There may be similar arguments for other pronunciation questions, but those I don't know.