This one doesn't have a frame swap but shows you how the truck should look from the side to be proper.
Cole Porter's old truck:
Note a few things:
1. Very important. The top rail of the bed is on the exact same plain as the running board and exactly parallel with it.
2. the bottom front edge of the bed side just fits down to the "stock" filler panel between the bedside and the running board.
Another and maybe better example of having the bed sitting right.
Raising the bed and lowering the fenders along with putting in filler panels below the bed sides would look rather hokey in most cases and make the truck look all wrong.
one way to do it though might be to set the running boards a bit higher and closer to the bottom of the cab to allow you to raise the bed a like amount. You would probably have to trim the bottom edges of the front fenders but it would maintain the looks of the truck. Easy to do on the frame swap too.
If you have to raise the bed to clear the frame to get it to look righ you have to raise the bed to clear the frame. Loosing load capacity is just one of the hazards of doing the frame swap and outside of a pair old lawn chairs and a cooler and a duffel bag most guys could give a rip about load capacity after a frame swap.
If keeping the bed floor at original height is all important I'd say go with the stock frame and a crossmember swap on the front and don't lower the rear all that much. As in any modifications you have to decide what you are willing to give up for the look you want.