I found a solution in only 8 intermediate steps:
It is possible that shorter paths still exists, because I couldn't obtain the complete MW dataset.
First obtained a word list
aspell -d en dump master | aspell -l en expand > words.en.txt
Keep only words that are 5 letters long
awk 'length($0)== 5' wordlist1.txt > wordlist2.txt
I don't find this terribly satisfactory, but it does kinda meet all the conditions.
has an anagram
which has an antonym
which ROT13s to
which has a synonym
which has a homonym
which is a part of
The last step is the least satisfactory one for me; the others all seem pretty good.
Here is my 10 letter word:
shearlings: skin from a recently sheared sheep or lamb that has been tanned and dressed with the wool left on
shearling: skin from a recently sheared sheep or lamb that has been tanned and dressed with the wool left on
shearing: to cut off the hair from
hearing: the process, function, or power of perceiving sound