All good suggestions, but I wouldn't go too crazy with the suspension tuning just to try to mitigate brake dive. These changes come with compromises, and if the bike feels good elsewhere, I personally wouldn't want to sacrifice that.
The reality is all bikes require some amount of rearward weight shift under heavy braking. Bikes with lower anti-rise just require a bit more, similar to how longer chainstays require more effort to get the front end off the ground, but it is something you can adjust to. I actually prefer bikes with lower anti-rise, since it helps the suspension feel more supple and active under breaking.
That said, if the bike is diving too much on sustained steep terrain, then that's probably something that should be addressed with some suspension, geo, or cockpit changes. I would start with raising the bars or adding air to the fork.
The one change that I would recommend that has almost no compromise in my experience is installing a Luftkappe in the fork to get a more coil-like spring curve. This adds actual position-sensitive midstroke support without affecting the small bump sensitivity and generally feels better everywhere (pumping rollers, pushing through berms, keeping the front end higher in the steeps, smashing rock gardens, etc.) in addition to reducing brake dive. You could accomplish something similar with a 3 chamber air spring (e.g., DSD Runt), although I haven't personally tried one. A coil fork is even better, but that does add quite a bit of weight.