Bad Response Times & down during backups (Molasses Plug-in seems to be working)

I am getting poor response times for a site. I have a dozen other sites on this server with no issues...

I am doing managed backups from 0300 and it seems to take several hours to perform a backup. My Memory is set to 384 MB usually peggs out and makes the site completely unavailable during backups. It is slow at other times.

I have WP Smush to decrease the picture sizes for file loads. I believe I have followed all of the recommended setting through the WPMU Dev plugins...

Current Server Info:

Disk Usage 1.46 GB / 4.88 GB ( 30% )
Physical Memory Usage 295.37 MB / 384 MB ( 25% )
Apache Version 2.4.25
PHP Version 5.6.30
MySQL Version 10.0.29-MariaDB
Architecture x86_64
Operating System linux