2005 Nissan Sentra 1.8 S...my mechanics can't figure out what's wrong with it

Since you took these problems to the dealer while the car was under warranty, and they weren’t resolved, they are still covered by that warranty. Call the Nissan regional representative with your complaint. Be polite, firm, and persistent.
Lack of a warm re-start can have a number of causes. A couple of suspects are: the fuel injectors leak fuel into the engine after shut down. This would flood the engine. One way to detect it is if the exhaust has a gasoline smell during, and after, the engine is cranked, and first started. To start a flooded engine (fuel injected, like yours), hold the gas pedal to the floor while cranking the engine. As the engine starts, ease off the gas.
The crankshaft position sensor (cps) is a suspect. It can be tested. A few minuets after the engine is shut down (the period of the greatest heat soak), the electrical resistance (ohms) is measured with a “voltmeter”. If they aren’t what they should be, the cps is defective.
Make that call to the Nissan representative.