RAT 5 has it pretty close for an all engine power loss. I'm not very familiar with the specifics of the 737NG, but with FADEC the throttle position is pretty much meaningless during a start - the FADEC is going to do the same start scheduling if the T/L is at TO as it will at idle. The important thing is to cycle the fuel switch so the FADEC is thinking "start", not "relight" (again, not familiar with the NG but on GE90 and GEnx the FADEC has a lot more flexibility when in start mode), and momentarily cycling the fuel OFF then back ON will often clear a stall or surge.
However shutting down an engine from power is hard on the engine - rubs compressor seals and such and can cause permanent performance loss. When we shutdowns and restarts during flight testing, we normally cool the engine at idle for at least 3 minutes prior to fuel off, then after it's running again let it warm for at least 3 minutes prior to advancing the throttle to avoid unnecessary deterioration.
An all engine power loss is assumed to be an emergency, so we're not worried about potential economic damage to the engine but rather in making thrust again as soon as possible. If the throttle is off-idle during the restart, as soon as the engine reaches idle it'll keep accelerating to the commanded thrust level.