CPU maxing out is definitely the cause here. A hard disk will not resolve it. You need more memory, and either cut down on the plugins and virtual instruments, or play around with the latency settings. One way would be to bounce any virtual instruments to audio as long as you are happy with the effects then you can run the new audio track without the need for any effects as they are embedded in the track.
Try opening the performance monitor under 'View' then tick show devices. You can then sort it by CPU to see the highest plugin CPU usage.
You would get improved performance from having your OS on a SSD and then using a good fast external USB-3 (or internal SATA) hard drive. Using a SSD for S1 audio is not particularly recommended as SSDs are not really very good for persistent write erase operations. It will be fast but the life of the SSD will not be great. But then if you have regular backups, it's not that expensive these days for a reasonable SSD SATA drive.
Having the OS on the same physical drive as Studio One is not a good idea. You need separate hard drives and preferably even a separate hard drive on a separate controller. I use a SAS RAID for mine, but not cheap.