What if you used the grey wire to operate a relay?
Their documentation says it is normally used to trigger a relay for a secondary fan when controller reaches its "high" setting. You could use it to drive a relay that bypasses the controller when its in its high mode, so the controller doesn't have to have to carry the "high" mode current.

And the other (more obvious) thing- what happens if you just put in a bigger fuse?

Oh, and another possible option- use the SPAL's normal output to control the low speed wire of the fan, and then use the grey wire to turn on the high speed when in "high" mode...