The OP did not suggest having side-loaded apps. For all we know, he's not familiar with the concept.

In any case, I suggest the OP sideload everything. "Nero Mobile Sync" comes stock with some Androids, and can be used to save the apps to the SD card. The apps can probably be restored after moving the SD card to the new phone, which would essentially be like side-loading them.

This is also a good approach if you don't like big brother (Google) keeping track of your apps.

Making backups of the apps is a good habit to get into anyway, because quite often you upgrade an app and find that it was really a downgrade (more ads or more spyware gets introduced). Backups are the only way to get back to the previous versions.