The penalty for shimming a square center leg to have half-rounded end pieces is 28.5% extra wire length, increasing copper cost and resistive losses in the same proportion. However you probably don't need full half rounded end pieces. About the smallest radius corners that would be windable would be 1 wire diameter radius. I believe from your photos the E lams are 2 1/2" across the center leg, and 4AWG wire is approx 1/5" diameter. Allowing for insulation, a 1/4" radius should be acceptable, and, assuming a square center leg it will only add 5.7% to the wire length required.
You certainly shouldn't be trying to wind straight onto the core. A former or mandrel is essential so you are only trying to bend the wire in one plane. If you are winding on a former the mandrel is essential to support it to withstand the crushing forces while winding . Ideally you'll want a split hardwood mandrel (with the split on the slant and both pieces waxed and highly polished) so when you move the halves in opposite directions to unwedge it, it separates from the coil or former easily. If you aren't using a former, either groove the mandrel faces or prepare the mandrel with lengths of linen cord with the excess taped down away from the winding area, so you can tightly tie (and glue) the wound coil to stop it springing apart when you remove the mandrel.
I did say in your other topic, that I'd probably choose to wind such a heavy coil from thin copper sheet (or heavy foil), one turn per layer, interleaved with Kapton tape for insulation. The depth of the E looks to be about 3 1/2", so to get the same CSA as 4 AWG wire you only need 10 mil (0.25mm) foil. Assuming Kapton tape of 0.1mm total thickness, you should be able to get over 80 turns on.