Paddy, what you have described make no sense to me. The statistics will always be perfect.
Whether you prefer to work in the Focus Window or the Records Window makes no difference to the File Statistics.
Switching between those windows will not affect the File Statistics.
You cannot count Media Records in the Focus Window, but the Records Window lists them on the Media tab.
What do you mean by it reporting a “more accurate quantity” and “initially was very unreliable”.
The count of Media Records (not Media Files) will always be perfect, just like the counts for all other record types.
Are you perhaps being confused by the largest Record Id associated with each record type?
There may be gaps in the Record Id numbers where records have been deleted.
So the File Statistics count will typically be less than the largest Record Id.
You say you have installed those Plugins, but have you run them, and what did they tell you?