Gmail – How to get push email with multiple Gmail accounts

I have a main (Google Apps Standard Edition) Gmail account which reads mail from 4 different Gmail accounts using POP3. The only problem I have is that it can sometimes take up to one hour before I get an email message, since the mailboxes are only checked about every hour.

How can I get the message immediately as it arrives, or at least very close to that (e.g. < 5 mins), while preserving the features I get by using POP3 access?

Here are the features I currently get by using POP3:

1. Robust auto tagging of Email based on the account they came from.
2. Account is kept alive.
3. Automatically chooses the correct address to reply from.

1: This is much more bullet-proof than simply creating a filter condition such as to:user@gmail.com, for several reasons. The first reason is that there are multiple valid aliases for each email address (e.g. user+foo@gmail.com or u.ser@gmail.com which would make the filter criteria complicated). The second reason is that I may have the mail account I'm reading reading mail from some other account (e.g. user.account2@gmail.com) so the to address would not even contain user@gmail.com. The same problem applies if I have forwarding set up to that account. Yet another reason is sometimes the sender will do really strange things like not having your email address in any of the to fields (e.g. when BCC'd), so the filter won't match. The point is, that when you use POP3 it is guaranteed to be tagged correctly. I have not found a consistent way to tag it any other way.

2: By logging in every hour or so, the account is kept from being inactivate due to Gmail automatically signing on.

3: When I click "reply" on a message, it automatically selects the correct from address (i.e. the email address that the email was sent to). This way I don't accidentally reveal any of my other addresses to the sender.