Log in to your primary Gmail account - don't create new Gmail accounts. In Settings, Accounts, click on "Add a POP3 mail account you own" and follow instructions. Uncheck Treat as alias. Repeat for each email address you are using, making sure to tick the Label incoming messages option. Once done, create the correctly formatted email signature. Bear in mind that calendar invites will come from the primary Gmail account address. Do this for all your staff.
You could stop there. The Gmail mobile client will work beautifully. Your send and receive email from each different address without having to think. When you search mail you have the fantastic Google search across all accounts, and you have one address book.
The Mail client has a small advantage over the iPhone in that you can specify the SMTP server when you are sending.
Therefore add your primary Gmail account and then follow this trick. In the "Email address" setting add all the email accounts separated with commas. Remember to add the signatures.
When you compose a message you can choose which account you are sending from, the correct SMTP server (you will need to add them all) and the correct signature.
iPhone Mail set up - Method 1
You only have to add the one Gmail account and add all the different email addresses in settings by separating them with commas. You can ONLY do this trick is you add the Gmail account as an "Other" account. It does not work if you add it as a Google account. Don't forget to add the different signatures.
When composing messages you will find that you can choose the correct account to send from. Unfortunately, it will put the message always through the primary Gmail account SMTP server. The recipient may see this personal address in the email headers.
iPhone Mail set up - Method 2
Add each different account separately. The phone is clever enough to detect duplicates but they arrive at different times. The first email arrives into the underlying email account and is picked up by the phone. A a few minutes letter, Gmail POP's the underlying account and a duplicate then arrives. The iPhone seems to delete the duplicate automatically.
The disadvantage is that the sent messages now appear only in the underlying email sent box and not in Gmail.