Attacking physics head on is going to be a bit hand-wavy, since we don't have the complete picture of a formal system that encompasses all physics yet.

How about for "the standard model" instead of "known physics"? That's a much better defined problem.

What do we know about estimating actual, stated-as-an-approximate-number-of-bits Kolmogorov complexities for formal systems which we can describe completely? Can we give an informed estimate about the number of bits needed for the rules of chess, or Newtonian-only toy physics?

Yes, we can (as long as you assume a particular instruction set). I don't know if anyone's done it, though. Also important to note that we can give upper bounds, but lower bounds are extremely difficult because of the inability to prove properties like "output matches physics" of programs in general.