some spots have gotten punky and I would like to know if using Clear Shellac (Zinsser Bulls Eye) is a good choice for stabilizing/hardening those areas.
It depends on your standard for hardness. But I'd have to say it's unlikely.
Some woodworkers use shellac as the beginning of their finishing method and it is readily absorbed by punky wood. In some cases it may toughen up punky areas enough that they don't need to do any more, but it depends on the variables.
Given this is a slab you're working on and some 'tabletop standard' must apply to the finished item, I'd think you'd want to use something quite a bit harder than shellac for the punky zones (assuming you decide to keep them) to provide the necessary durability1. This goes double if any punky areas are along edges.
I would tend to use superglue for this and thin superglues are widely used in various areas of woodworking for this purpose, woodturning especially.
But just how soft your punky areas are should probably be your guide — if they are truly soft and spongy, as opposed to just like a much softer wood than the unaffected madrone, I think it would be preferable to dig them out and replace with filled and/or tinted epoxy.
Should I just dig all these areas out and fill with epoxy or is the shellac a good way to fix these spots so I don't have to dig them out and I can keep the slab's natural look and color?
The guidelines on SE are to avoid asking subjective questions so we can't really answer this sort of query.
But I will say that such fills don't have to look completely artificial2, with the right colouring they can easily be made to pass scrutiny from non-woodworkers (who are unlikely to look at them twice). And with a little more care and attention you can do fills that even woodworkers can't spot, or at least their eyes aren't drawn to.
With the black squiggly separation lines and changed colouring in some enclosed 'cells' it's not too hard to come up with epoxy fills that tone-in with the surrounding oddball colouring.
1 In general shallac isn't hard enough to begin with, and doesn't cure hard fast enough anyway — I know this will likely seem contradictory given shellac's well-known fast drying time, but it takes far longer than its initial drying time to get to full hardness. And IME shellac actually does so little to harden up punky wood that I'd never rely on this myself, even for a decorative item I'd prefer to use something that is much harder.
2 Honestly though, since you're already planning on using black epoxy for filling cracks and voids I think the all-natural look has already sailed!