I've got a Sears Craftsman (Murray) 30" riding mower. Per the manual
the replacement blade is a 56060HT.

Searching for this model online I'm getting many hits plus more that
cross reference a newer series. Then comes the confusion factor as
these blades often have different center hole sizes, .850", 7/8"x1"
and 27/32. Even the original blade depending upon website may list
any one of the three.

Are all three sizes truly interchangeable?

Yes, they a Considering tolerances, they are all the same size.
7/8 = .875
27/32 = 0.84375
where 0.850 is the manufacturer's nominal, most likely.

The "play" I've seen in most blades is in the order of 0.100, so those
all easily fit within that. The 27/32 would be the closest, ignoring
tolerances.