NPR's Word Puzzle

NPR's Sunday puzzle last week was the following: find a five-letter word in which the position, in the alphabet, of the first letter is equal to the sum of the positions of the last four letters.

This week they gave the following answers: maced, table, whack, and zebra.

More generally, one could ask the same question for words of other lengths. Here are a few I found:

cab
hag
jade
leaf
leg
mage
mica
mid
need
pig
rale
real
ride
same
sand
seam
toad
toe
vial
vim
weeded
wend
who
wick
win
yet
yip
zeta
zinc

So "weeded" seems to be the longest word in English with this property. Can you find a longer one?

They also talked about words like "easy" in which the position of the last letter is equal to the sum of the positions of the preceding letters. I found the following other examples:

abbot
ally
away
babe
bail
bendy
bidet
bleat
boar
cachet
debit
dim
draw
eager
fag
feces
flew
gnu
habit
hair
hem
hoax
how
idly
jaggy
joy
kit
lam
man
neat
pact
paddy
sex
tabby
tau
wax

So the longest seems to be "cachet". Can you find a longer one?