Here it is, no explanation needed i think :)
As @IvánNokonoko mentioned in the comment, the NNE grid in the second layer (from outside) can also be R instead of A to form (GRIT and BRIT). Thanks!
Completed octogram and the word at the bottom:
(I know you gave us an answer template, but I like the pictorial format!)
The puzzle is actually in two halves (plus finding the bottom word), and each half is easy to complete once you find the first short word in it. Given one short word, say from long word A to long word B, you can easily ...
Deducing $c, f, h$
regarding B, C:
only pair available for distance of 4 is:
Sum of 25 rule renders
Deducing the rest
regarding A, E:
only pair available for distance of 2 is:
Sum of 25 renders
OK - here is a real solution this time without concatenation.
I have a couple sub expressions.
Now I can construct $A,B,C$.
Not sure if this is in the spirit of the puzzle since I am using the fact that $1 \div 1 = 1$ and getting a set of pan digital sub-expressions which equal to 1.
EDIT: I've added some other possibilities which don't bear as much ...
Partial answer that I'm saving for now
(For convenience, I will call $PCRON$ "the root" and $PRINCETOM$ "the square".
We can first deduce that the digit N
We can also do some quick tests to find the approximate range
Let's try that:
We can then determine that C is