The problem you run into is that the project is longer than the table and you cannot support the work piece. This is a common problem, so you’re not alone. Unless you work in a cabinet shop, you are going to have to figure out a way to support your work piece. You can always go out and by a roller stand for the support. I recommend setting up some sort of bench stand. Even boxes that help hold your work piece have worked. The whole idea is to make something work and then take it apart. Again this is very common.
Cutting the grooves is left best to two different tools. The first is the table saw. You really need to have a dado blade set up in the table saw to do a decent job that will not take you all day. The table saw allows you to cut the grooves in one or two passes. Again because the pieces are larger you will have to fashion some sort of support. The other tool you can use is a handheld router. You will need an edge guide for this method. An edge guide is a nice tool that is basically a straight edge with a clamp built into each end. You can even substitute a straight piece of wood if you do not have an edge guide. You will want to install a straight bit into your router and line up the edge of the cutter with a line you have drawn on your project. Next clamp down your edge guide so that your routers base plate will move along the cut line as you have it drawn. It only takes one complete cut before you will be flying through this type of joint. The time is spent in the setup and in figuring out how you want to make the cut. Make sure you only take the stock out in small bites so as not to bog down the router. This is better for the tool and for your router bits.