For Strapping, I copied the method Peter the Quick posted
here.
Did it for a kite/teardrop punch. It seems to hold up pretty well, but the punch grip complicates things somewhat since prevented my elbow strap from being as close to the center as I would have liked, but this should be less of a problem with rounds.
If you can't find good planks, you could try making the shield purely out of blue. There's a good tutorial on how to do it on youtube. It eats up a lot of blue rolls and DAP though, which probably makes it more expensive and definitely more time intensive than carving up a plank.
For the tower shield, depending on the exact dimensions you want, you may look into using a Thrift shop boogie board if plank foam in not available.
Hard to * up a wooden core round, not to mention they last forever. A 28" round, which would have a 24" core is the catchall standard. A progressive build as well as decent tap will help keep the edging from going.
Use T-nuts to make straps easy to remove for repair and don't forget to pad the inside. Aizen, bearer of the peanut shield, strapped his round so that the elbow is closer to center. He likes how it protects him better from wraps/flails and gives his arm better maneuverability.