Gmail

Are you sure they're actually being sent to the Trash bin? By default they get Archived (sent to "All Mail") so you might think you're deleting them but they're actually being archived. Check your iPhone settings for the GMail account to see if "Archive Messages" is ON or OFF. If you want to send mail to the Trash, turn this OFF.

If this is turned off and mail is being sent to Trash, there is no reason for your trash to be emptied by you just navigating to the Trash folder on your iPhone. Trash gets emptied automatically (by Google) but not by you navigating to that folder.

OK, now I know what your problem is. I too used to have my GMail set up as an Exchange account, and was happy I still had it even after Google stopped supporting it for new installations this year. You're correct in that when you set it up as Exchange there is no setting on the iPhone to route deleted messages to Trash, the setting for that would have to be made on the Google server side (m.google/sync) using Safari right from your device.

However, once Google stopped their support of Exchange ("ActiveSync") they also reverted the Trash setting to Archive, and they removed the ability to change it back to send deleted messages to Trash. You can verify this yourself by going to your "All Mail" folder -- you likely have a few months of messages in there that you thought you deleted. I did, which is why I went back to the standard iOS GMail profile which lets you change this setting (I'm not that concerned about losing Push notification).

Oh, and if you're worried about losing the sync of your GMail Contacts when using the standard iOS profile, you can get that back by following this instruction:

http://support.apple.com/kb/HT4872?viewlocale=en_US

Did you confirm that your "deleted" messages are actually getting archived to All Mail? If that's what is happening, then no there's nothing you can do unless you can qualify for a "business" type of GMail account, those still support ActiveSync.

If you can't or don't want to go that route, then give the GMail app a try since that does send deleted messages to Trash and supports Push, or use the standard iOS GMail profile.

You're welcome, sorry that there isn't a better solution.