I would agree triggers sound bad.

You have a process here, and you are storing data, not calculating on the fly, so likely there isn't something built into SQL Server for this.

I would modify the SSIS process perhaps to make this run smoother and recalculate the changes only. Either take a look at the way you change data, and perhaps modify/calculate inline in the SSIS package and then just send the updated values for everything in SSIS.