Money Orders deposits via ATM won't work for all applications, but it should work for most.
Warnings about MO's & bank accounts:
Always keep copies of everything you do and get receipts where possible. This way if something goes wrong you have a paper trail to help rectify the situation.
Start small and only do amounts you are comfortable with having frozen, in case of a shut down or dispute.
Check that the bank is FDIC insured or has NCUA insurance if it's a credit union.
Spread your money orders around different accounts.
If you sign up for a new bank account be wary of monthly fees and early account closure fees (most banks charge this if you cancel your account within the first)
Some banks will do a hard credit pull when you open a new account, all banks will do a ChexSystems inquiry.
Too many ChexSystems inquiries in a short time frame can result in a fraud flag or similar being placed on your ChexSystems account. This will make it difficult to get accepted with other banks/lenders that check ChexSystems.
It's also a good idea to familiarize yourself with structuring laws to ensure you're not violating them.