Exceptional workloads filling Tier 1

I get the feeling there's no good answer to this, but I'll ask anyway.

Our normal SQL server workload onto our SC device leaves plenty of spare space on Tier 1. Occasionally though we have to run large write jobs treble the usual amount of daily writes. This leads to Tier 1 filling up with data that really ought to go straight to Tier 3 as once it's done it highly unlikely it will be read again. Think data redaction.

When this job runs the normal production workloads suffer because they have to go straight to Tier 3.

Any suggestions beyond a vastly bigger Tier 1 just for these times or reworking the SQL database to move this data so it's already on Tier 3 before it starts? DB is outside of my control.