I have a very similar problem.
I am running a full backup of a 4TB database. For months the backup succeeds with little impact on the rest of the system. Of course it takes multiple hours.
Now, suddenly the backup core service is using 100% of 8 cores for the entire period of the backup.
The backup is set to create 8 files so the file sizes are manageable (each is ~50GB). Compression is set to Level 3. CheckSum and Verify are OFF.
According to Perfmon, SQBCoreService is using an average of 400% processor with a maximum of 500+. Perfmon also shows all 8 Cores at continuous 95% plus User Time.
Update: This was not a Red Gate Backup issue.
I spent some additional time analyzing this issue and I have determined that there is not really a specific problem. The database is 4TB and I am backing it to 8 files (all on the same disk). The server has 8 cores (2 x 4). The final files are around 40GB each (+/-15GB). The backup takes about 4 hours when several major application activities are shut down. When those same activities are running the backup can take up to 7 or 8 hours.
Right now, with just normal application processing in progress, I see that all 8 cores are consistently well-over 60% utilization and the Average %Idle Time for each core is in the 20% - 30% range.
So the issue here is clearly that the processors are just at overload under normal circumstances and adding the full backup just drives them to saturation