You don't have to melt through that adhesive - it's incredibly weak and you can just pop it out with a sufficiently thin pry bar. This guide [1] does it with an iSesamo, but I just used a utility knife since I had one on hand and wasn't particularly concerned with scratches (the entire seam is covered by the headphone pads, so scratches around it are invisible).
The only AF systems that use LIDAR are the one on the newest Hasselblad medium format mirrorless cameras (since DJI owns Hasselblad and can leverage the tech from drones/cinema cameras) and possibly some phones.
I suspect it's fairly challenging to implement since the LIDAR sensor doesn't operate through the lens, so you'd have to continuously align the depth map with the image to account for parallax; plus it's only useful for close-ish distances (since the lasers can't be too powerful) and can cause unwanted focus behavior with windows or reflections.
Replacing the batteries on the Maxes is actually a fairly straightforward process (no adhesive melting required, just a screwdriver and a pry bar), and spare batteries can be purchased on Amazon or Ebay for around 50 USD. It's one of the better Apple products in that regard, very unlike the in-ear models.
It's nice to see some high-performance linear algebra code done in a modern lanugage! Would love to see more!
Is your approach specific to the case where the matrix fits inside cache, but the memory footprint of the basis causes performance issues? Most of the communication-avoiding Krylov works I've seen, e.g [0,1] seem to assume that if the matrix fits, so will its basis, and so end up doing some partitioning row-wise for the 'large matrix' case; I'm curious what your application is.