With an acceleration ramp and plenty of vertical and horizontal surfaces to employ, there are many possible portal paths that can accumulate the requisite speed and angle to smash both buttons before hurtling into the exit sequence.
The long upper corridor can serve to regulate most remnants of the ramp’s randomizing influence. While I found this route to be the most efficient, plenty of possibilities exist to use the angled deflectors and chambers for a similar outcome.
Extra challenge points:
- use the oddly-shaped chamber (upper left) somehow
- exit upside down and/or backwards
- reuse a portal