Did'nt the Phrygian language survive well into Roman times?
The language died out between the 5th to 7th Century AD. That doesn't mean there were significant numbers of them left by that time. There are still small villages which speak Aramaean today, but that doesn't mean there is a viable Aramaean population out there which has any chance of successfully rebelling and restoring their independence.
The Phrygians as a political entity died out following the Cimmerian invasions. Even at that earlier period, while they were independent, Greek influence in Phrygia was quite strong. There's no real evidence they WANTED to resist Hellenization.
If you can do something about the Cimmerians...have them go east into Iran rather than west into Anatolia, for example...you might get a longer-lasting Phrygian polity that might be locally powerful in Anatolia for another hundred years, until the rise of Persia in the mid 6th century BC. The Kingdom of Lydia won't arise in that scenario, but other than that, actually very little changes. Instead of Croesus of Lydia facing Cyrus of Persia in 547 BC, you have King Midas VI or Gordias V of Phrygia instead. The result is almost certainly the same.
Once the Persians came in, the last spark of independence among the Phrygians died. They were viewed by the Greeks and Romans, from that period onward, as passive and dull, and pretty much accepting of whatever ruler took control of the area. Not prime material for a rebellion.