Let's think about this direction a little. Essentially we want tabs belonging to different browsers to live together in a "virtual, meta browser", say, Browser X. In Browser X, you can specify a particular browser (e.g. Chrome) to handle new tabs by default, but you can also create a new tab with a specified browser. This can be easily implemented by a "+" button and a dropdown menu to the right of it: if the user clicks "+", a new tab will be opened using the default browser (Chrome); if the user clicks the dropdown menu on the right side of "+", there will be a menu of all browsers where the user can choose one for opening a new tab. Once a new tab is opened with a specific browser, that browser's extensions can interact with the user and this tab.