Hey James,

To drill down into your request:

"We would like to enable our end users to find the last run time of their connector from within our database"

Using the "log" table within the Fivetran Platform Connector schema, we give many log events that could be useful here. Please refer to the full list of log events here.

For example, you can use the "sync_end" event to enable your end users when a given connector has finished syncing. Additionally, you can even filter for events like "alter_table" which tells you when table columns were added to, modified in, or dropped from the destination table.

We even have almost plug and play sample queries available to help.

E.g. 
Check sync start and end times
Check records modified since last sync
Check daily modified records
Review records_modified count data by table

Hope this helps.