By your own numbers, this could translate to a 30-second AES key exfiltration in the cloud. This isn't a non-issue, even if you personally aren't affected.
you have to find the address first, which is a lot of rummaging around. you aren't just handed it. that is going to quite a bit, especially the program build any security measures in (eg, allocate at a random address). good luck with that.
it's easy to say vulnerabilities don't matter... when responsible disclosure results in fixes for those specific relevant systems for which actual executable Proof of Concepts were designed. The authors have the skill and knowhow to do this for new systems, and the surrounding knowhow and skills are not gained by merely reading the whitepaper that focusses on the exact nature of the side-channel. Similarily a paper from the field of say physics, will not hold your hand by having a huge appendix filled with the physics courses, exercises, ... the authors enjoyed as a student...
Spread the key over a whole page with fec, implement the key recovery using non saved registers. Would be nice to avoid pre-emption and avoid leaking regs to ram. Perhaps last step could use avx to run a permutation.