That sounds reasonable... however, if banks are not allowing cash deposits into personal accounts anymore (as someone said here), having several accounts in different banks is not solving the problem (unless of course one of those accounts is a business on where cash deposits are allowed). In my case I file taxes as a sole trader (no company) and have one account (personal), I've been depositing my earning the last day day of each month for years religiously. Last time I did this I was thoroughly interrogated as to were my cash deposit came from. I thought it was weird (they've never asked me anything all these years), so I'm thinking in opeing a business account with another bank.
If you only pay in once a month I'm guessing it could be a large amount, which may then be more likely to be questioned?
Cash deposits by account holders are fine, it's cash deposits by third parties which was stopped earlier this year.
Has to be the account holder, have you thought about using ATM pay in - a few banks offer this, and or the post office? Many banks can be paid into at the post office.