I would definitely recommend setting up the bandwidth limit for site servers during whatever time windows you require. We have a 50KBps limit during our working hours and unlimited out of that. These settings are held under 'Settings > All Settings > Agents / Plug-ins > Symantec Mangement Agent > Settings > Symantec Management Agent Settings - Targeted'
Select All Site Servers and then Downloads from the Tabs and enable Use bandwidth throttling.
Add throttling periods you require and setup the value to whatever your sites can cope with.
Its the only way to get around it. I've not found that i could force the devices to talk to just one server however the way i've got around that is to add the new sites subnet in to the main site's subnet list.
The new server believes its at the main branch and will talk to those site servers primarily before going else where. This would do what you want and once it has the first set of packages move the subnet back to the new site and it would work like any other.