Yeah, I also looked at the problem in the book (wasn’t able to google the solution) and it seems that the problem is just badly worded. I think the only way to figure out the last names is to make the assumption that the biological son is going to inherit the most.
The answer you gave matches what I was thinking, though Eliza & Susan could be swapped (and still no reason for why Smith gets the most).
The other possible solution - following from Bi = 2116, gives
Ja/Ja/El/Su 4
Sa 3364
To 6724
Bi 2116
Ma 5476
Ne 8836
El/Su/Ja/Ja 9409
Su/El/Su/El 12769
Ha 16129
where the slashes indicate a possible swap.
What a horrible solution that wil be if that’s the answer! 
But you may well be right.
panamajack, your solution, with the swaps, looks somewhat like what I ended up with. I eventually found a way of arranging the nine values such that I couldn’t see where any rules were broken by it and stopped there, but I was pretty sure there would be alternate arrangements.
I’ll go home tonight and look at my notes to see if the solution in the back of the book matches what I came up with. If not, it’d be interesting to try to figure out what distinguishes one from the others.
Thanks, folks, for looking at this with me, and keep on offering your thoughts on it! This puzzle literally made me lose sleep for a couple of nights, as I’d go to bed, not be able to stop thinking about it, and get back up and work on it some more.
Daniel