I'm used to seeing 400-600 CCA (and less) out of a new car battery, but it's been at least 10 years since I've spec'd a battery. Battery technology has progressed a lot since then, so I wouldn't be too surprised if those numbers are in the ball park. Sounds like over-kill for a small engine with the ability to alter valve timing to me, but I'm old school.
A lot depends on the test equipment and the person running the test, but if you used two different places, I'm inclined to believe them.
Given those test results, I think it's safe to say that the battery is not the problem. Which leads me to believe that your mechanic doesn't have the slightest idea what's going on. I don't either, but I'm not getting paid to know.
Unless you have a dead short somewhere, you can't have too much ampacity; the car only draws what it needs.