Men of Moments (edit 1)

[Brownlie]

I would add some punctuation.

He said he was
barbecuing chicken

My Mom would usually
chop them into stews
that would last

My Step-Dad
was working again
and on a good run-

wasting them
for one meal
was a statement

A man of moments

I grew up enough
to throw him down stairs
and out of houses

We ate vegetable stew
and listened to pastors -- More can be said about pastors or the type of pastor can be specified. Maybe physical details about listening to pastors or quotes from them or something. So long as you don't damage your tone here which is not bad.

He lived in cars
and on concrete -

not like
the Volkswagen Rabbit
he wore flip flops
and corduroy shorts in --- This section would really benefit from punctuation.
that cranked Boz Scaggs
and The Little River Band
when we met

When the garbage men found him
behind a dumpster
wearing his liver on his jacket
my Mom paced for answers

I listened
to Boz Scaggs
with Jim Beam

Not bad, I like how you used the proper nouns. I think you may want to consider adding punctuation though.