Deleting the .mq files means you are deleting polled data that has yet to reach the SQL Server, which then means you cannot report or alert on the data you dumped.
What I sometimes do is stop the Job Engine v2 (service responsible for polling all data), then wait to see how long it takes for the MSMQ to clear out to the SQL Server. The MSMQ is great in case the MS SQL Server is unavailable, because the services will hold onto the data until the SQL Server is established, or availability to the SQL Server is available.
You have SAM already, so I would recommend using the AppInsight for SQL to monitor the SQL instance. It can report back all performance data, which will be useful to the Database team.
We cannot give any other recommendations without the sizing (CPU, memory, Disk RAID configuration) of the MS SQL Server.