Contract based job affecting bank lending

[Andrew Mengele]

I have been applying for mortgages and lending recently and have encountered a hiccup. 

My job traveling doing specialty commercial construction is contract-based - meaning sometimes I work for a few hard months and then have a month or so off between projects. Similar to traveling nurses who I have heard have similar issues with loans. 

I have a good chunk of liquid capital saved with almost an 800 credit score with no debts but banks won't lend to me because my work isn't predicable/traditional. Any advice? I was looking to do a 3.5% down FHA loan but am now considering a traditional 20% with a property I recently found.

Any suggestions appreciated!