Give Coyote a buzz, he had a very similar problem, and found a competent tech to fix it somewhere... This is an excerpt, which makes sense:

I experienced a similar problem. Turned out that the auxiliary water pump,
for the intercooler, needed to be replaced. This caused an over temp issue
for the supercharger, so it didn't engage.

Coyote


I remember he went through hell too... Had to get the "super-tech" down from somewhere to finally analyze and get it fixed... If it happens to be the same problem, suggest having Chrysler do a TSB on it since it's happened to a few Xfire owners... But his was an SRT6 though, and I believe you have the Limited without the supercharger, so this still may not be correct...