Dennis, there are a lot of ways to accomplish this. They do make a protable band saw that is often used by people like framers of post and beam structures. Have no idea if you can find one to rent but I do know that the same saws are also sold by machine shop and industrial metal working supply houses for cutting samples and the like. You just need to change the blade.
Once you get the beam cut to rough shape, you can cut a pattern and use your router to clean up the cut. There are several ways to do this, depending on the bitt you have. Pattern following bitts with a bearing at the top are probably the easiest to figure how to use. They also are more fragile because of extended length and expensive. Putting a collar on a plunge router baseplate and using something like a 1/2" up-cutting,straight bitt of solid carbide is probably the safest option as you can use the plunge feature to cut in several steps. Mount the pattern with small brads of double stick tape and work from both sides by moving the pattern.