I am not fully understanding you. I think you have an oval table that you want to "belt" with a contrasting 4" strip, girdling the edge of the table right? So hypothetically speaking, if the inner oval was 128" long, and you slapped the strip around the table, you'd have a total dimension of 136" ?
You could possibly heat or steam the wood, but 4" is a lot of wood to bend, steamed or not, especially for someone who doesn't have a hydraulic press or the like. This lip really has to be 4" deep?
1) You might be best off curve-cutting a larger flitch to dimension and attaching it that way. You are looking at a fair amount of waste in this method.
2) alternatively, you could bend and glue up .5 to 1 inch strips and build up the edge to 4", but that is a lot of glue interfaces where things have to be fitted well.
Hope someone else can think of something I am not.