How can I force new browser windows to open on my main display?

Have you tried running your browser in fullscreen mode? (Using the 2 diagonal arrows button in the upper right corner of the window)

I have a very similar setup and it works exactly as you are asking.

• MacBook Pro connected to a Thunderbolt Display
• Thunderbolt Display is the primary (with the Dock), MBP is secondary
• Chrome running on the MBP screen in fullscreen mode
• ⌘+Tab to Chrome, which activates the app on the MBP screen
• ⌘+N to create new Chrome window, which appears on the primary Thunderbolt display

Right click on Chrome icon on your Dock, select "Options", and check that you didn't have Chrome assigned to a specific monitor. You can select "None" or specify your main monitor, as you prefer.