Iron Age Thracians are more Eastern and Southern compared to Bronze Age samples from Bulgaria. Sure that E-V13 was common among Thracians so far but that Thracians are the main source of it I highly doubt but of course I am willing to change my opinion. To me it simply seems E-V13 is a general Y-DNA that hit the boom, it happened earlier among Thracians and then later among the rest of Europe and Balkans.
J2b2 hit a bottle neck effect already during Cetina this does not mean that J2b2 did not exist outside Illyrian sphere , the correlation with J2b2 and Illyrian however I believe is stronger than E-V13 and Thracian. Let's not forget none of these Y-DNA ever came from the steppes most likely so Steppe people were R1b
E-V13 had its largest expansions when the Thracians (Channelled Ware-Stamped Ware and Thracian Hallstatt) expanded, not earlier, not later. That's clear from the data and indisputable. There was no later expansion which was even remotely as big.
The difference is also that J-L283 seems to have spread earlier to other people (!), while E-V13 seems to have not (as much, if at all).
So Illyrians were for the most part J-L283, but not all J-L283 Illyrian, even in the early stage. For E-V13 it seems that the total majority if not all E-V13 carriers were initially Thracian - regardless of E-V13 being the only lineage or not.