Here just another map for what happened in the Late Bronze Age, Channelled Ware/Gïżœva related groups came down from two directions:
One from Gïżœva directly, they did took the Eastern route, the other from Belegis II-Gïżœva, which is basically a Gïżœva daughter culture, but some authors stress differences, while others don't.
This leaves only two options:
1) The original Gïżœva were already rich in E-V13
2) Belegis II-Gïżœva was the main carrier, either by picking it up from locals - since local influences came into Belegis II-Gïżœva, or by founder effects on the way. Like E-V13 could have been strong in Gïżœva already, but got even more dominant by later founder effects in the Belegis II-Gïżœva daughter group.
The earlier groups of the region, like Paracin, Brnjica, surely were also more closely connected to Gïżœva than to the Western, Illyrian neighbours. One of the main distinctions is in the ceramic assemblage and the burial rite, which was for the Gïżœva-related people and their ancestors for thousands of years most of the time cremation.
As one can see, since descending down from the Tisza-Danube area, these Channelled Ware people were always in close contact and neighbourhood with Illyrians, with which they mixed. Sometimes as adstrate, sometimes as substrate, depending on region and period.
Therefore it is absolutely not suprising to have J-L283 in Thracians and E-V13 in Illyrians in the later periods. Anything else would be a surprise. Actually they even went on together in some regions and for some campaigns, possibly, like in the Sea Peoples adventures. The Northern Greeks-Dorians also look like they might have gotten influences from both (Illyrian core Tumulus, Middle Danubian Urnfield and Gïżœva-related).
But to make this absolutely clear: Some sporadic stray finds of singular E-V13 carriers won't solve this. At that time, there were many thousands of E-V13 carriers around, and they grew rapidly in numbers from the LBA to the MIA, only some dents can be recognised, caused by foreign invasions. Typically invasions in Pannonia caused a downfall (Cimmerians, Scythians, Celts, Romans). That alone is quite telling as to where the bulk of them was living, in Eastern Pannonia/Carpathian basin and at the Danube with its tributaries.