Yes, for most spins, it's the build up of speed during the recovery which is the danger to the aircraft structurally. The challenge is, while the plane is pointing just about straight down, allowing it to accelerate enough to not "secondary stall" it upon recovery, but not so much that you overspeed it.
This results in one of the other things we look at during certification, upset. If the pilot does something silly in the plane, and ends up pointed straight down, is there enough margin between the speed they were flyinig, and Vne to allow them room to get out of it without overspeeding.
The added challenge with the dive is that as speed builds, the desire to get out builds, and the G force being applied to get out increases, so the stall speed increases, and you're back to the secondary stall problem again.
The accelerometer installation for my spin testing was a bit more straight forward than you suggest. You want something which is really easy to read, when things are changing fast!
(That
is the reading after my first spin testing, I purposefully did not reset the recording pointers in flight)
