There are 2 ways to machine something. You either take the work to the tool as you are trying to do, or you take the tool to the work which is usually done when the work is big and hard to handle. If the bit has a bearing you can do it freehand with just router. If it doesn't do it freehand using an edge guide or a straight edge clamped onto the boards.
The other option is to build infeed and out feed platforms to help support the pieces on the table.
Someone I consider a master woodworker once told me that a master woodworker is not someone who never makes mistakes. He is someone who is able to cover them up so that no one can tell.