How can I transfer purchased apps to another Live Account?

I'm not sure if this will work with your account scenario, but I have done a similar in the past with some accounts of my own.

If you already have an old and new microsoft account, migrate the xbox gamer tag to the new account.

1. Log in with the account you want to change
2. Go to Settings and select Account
3. Scroll right to Your Information and select Account Security.
4. Select Microsoft account
5. If you already have another Microsoft account, select Yes, otherwise create a Microsoft Account
6. Enter the password for the Microsoft account that is currently associated with your gamertag and select Sign in
7. Enter the email address and the password for the new Microsoft account that you want to associate with your gamertag, and then select Sign in
8. Select Yes, change to change the Microsoft account associated with your Xbox LIVE account
9. And Finally, Select Update Contact Information to update your contact information or Done to finish

These are the steps that I took to transfer phone contacts to another Microsoft account. I did not have two existing accounts though and do not know how it will work in your exact scenario.

One caveat is that you will have to re-download all content manually. When you go to the store, the buttons will still say buy, but once you tap them it will provide a message to the effect of "You have previously purchased this already, do you wish to download?". You will not be charged again.