Alright ya'll, this wasn't my best moment, but I discovered a simple shortcut to completing the time trials whilst raging. You don't even need a specific build for this.
Play through the trials to the best of your ability, but don't sweat if you're running out of time. When the retry/leave screen appears upon failure, pop out your battery pack (or batteries), then pop them back in.
You should see a window that asks you to reconnect your controller. Do so, then choose the 'leave' option on the failure screen.
Whatever rings you have left will still appear, but the timer is absolutely gone. Now it's just a matter of getting through the rest and it'll count as a completion when you pass through the final ring.
Long Story Short: Fail the trial at any point, disconnect/reconnect your controller, 'leave' the trial, continue swimming through the remainder of your rings to completion without a timer.