Just set up a "forward everything" rule from your apps account to your personal account. Then use labeling in your personal account if you need the separation.

Just set up a "forward everything" rule from your apps account to your personal account. Then use labeling in your personal account if you need the separation. For outgoing mail, add your apps account under "Accounts and Settings > Send Mail As" and check "Reply from the same address the message was sent to." I have 3 apps accounts and 1 personal account. This has worked out pretty well.