A normal trans service will not fix an engine stalling out the issue. This needs to be fully inspected by a qualified shop.
Use this link to find a good shop near you.
https://repairpal.com/repair-shops
Alex
RepairPal Certified shops can diagnose and repair your 2004 Chrysler 300M. They provide transparent pricing with a minimum 12-month or 12,000-mile warranty on repairs and services.