I don't see why you can't create a Push option for the stock mail app. Its under settings in the Check frequency option of Sync Options.
Anyway this is what I recommend doing, it will also save your battery as you wont have multiple emails syncing and you get a nice app with gestures too.
Forward all your emails from your old email, lets say
mac@hotmail.com to your gmail account.
Go into your gmail account (in a browser) under Settings and then go to Accounts.
Add another email address and save.
A email will be sent to your address
mac@hotmail.com address requesting permission to send emails from your gmail as if it was sent from
mac@hotmail.com
Sync only the gmail app.
Now everytime you reply or create a new email you will have a drop down option to select which email it is From ala K9 style but a much improved app.