I found a solution in the Firefox source code - loadTabs.
Instead of loadOneTab I used this:
window.gBrowser.loadTabs( [linkGo] , {
inBackground: event.target.inBackground,
relatedToCurrent: true,
allowThirdPartyFixup: true,
triggeringPrincipal: services.scriptSecurityManager.getSystemPrincipal()
} );
Instead of loadURI I used this:
window.gBrowser.loadTabs([linkGo], {
replace: true,
allowThirdPartyFixup: true,
triggeringPrincipal: services.scriptSecurityManager.getSystemPrincipal()
});
…The key is replace: true, which makes the URI open in the currently open tab.