The gurgling you’re hearing may not be a symptom of the overheating. It may just be the blend door actuators on their way out. Mine’s been doing that for years.
When the engine starts to overheat have you checked to see if both the fans are on? Nothing impeding air flow through the core? Overheating while idling makes me think fans, blocked core, or tstat. You may want to get some coolant in there just so you might smell it if it’s leaking somewhere. And like said in an earlier post always bleed from the expansion tank by the turbo.