So does this mean that you have your Gmail account setup twice? Once as IMAP and once as exchange account?
This seems like a hassle.
When you setup Gmail, either as IMAP or exchange, does it allow you to synchronize contacts. Just set Contacts to on in the Gmail settings.
Also, you can always change the account you are sending the email from. Simply use the email function in Photos, then tap on Cc/Bcc, after that on From: and choose from which account you want to send the emails.
And finally, both the IMAP as well as the Exchange setup will delete emails on all devices. So if you delete an email on the iPhone, it will be deleted from the iPad as well. If this is not the case on your iPad, you may have to check the settings.
There is really no need to have two gmail accounts on your devices, as either setup has the functionality you are looking for.
You probably already know how to setup Google as an exchange account, but if you follow these instructions, will it synchronize all email deletions/moves across all your devices:
Setting up Google Sync with your iOS device : Mail, Calendar, & Contacts - Google Mobile Help