Start diagnostic data collection as early as possible

Currently diagnostic data collection does not begin until fairly late in the startup sequence, after some potentially significant activity such as oplog stones and interrupted index builds have been done, so it can't be used to diagnose problems early in the startup sequence. Ideally it should be started as early as possible; one dependency is storage engine initialization since it collects WT internal statistics that won't be available until the storage engine is initialized, so maybe it could go right after storage engine initialization.