This requires a little bit of work but we might able to get it to work. the first thing that needs to happen is remove the Shipping Server behaviors that are on the confirm page. There should be about three of them (you could just comment them out: 356 - 570).
You will then add your select list with the three options. And then on the confirm page you will set a session of the value of the type of shipping selected. and you will use that shipping in your eCart object to set the shipping rule.