Towel method: Uncontrolled overheating warps the motherboard, melts plastic, and can cause fire. It may temporarily reseat cracks, but they recur worse.
Real Fixes
Professional reballing: BGA rework station replaces solder balls with leaded alloy (~$60–$100). Lasts years.
X-Clamp replacement: Improved pressure distribution (moderate success, requires skill).
Replace the console: Refurbished 360 S/E models are cheap (~$50–$80) and reliable.