Great looking setup Jason. I went through the whole thing too with the Gator. Here's the deal: I used the standard "coaster brake" axle on the Simplex dropouts with steel axle bushings. You may have to order a longer rear axle shaft 'cause your drops are wider than a standard bicycles. Your Sturmey A. rear axle's about the same size i.e. too small without the bushings. My Springer fork uses a small axle as well. My question is: What are you trying to achieve with a larger axle diameter? Perfect fitment? Then use bushings. Perfect duplication of Simplex design? That's good too. Or is it about safety as well? That's really important in my mind and I stayed with the smaller axles. My reasoning involves the current state of product liability laws & a the state of our current society. Companies overbuild even the cheapest Walmart bicycles because of fear of litigation. If you are a normal size guy say between 150 & 250 lbs. the 14 ga. spokes and axles on a Wally bike are sufficient, but the spokes and rim will go before the axle. Jason your Worksman wheels were made to haul industrial loads and pedicab passengers as well as for pleasure use. The same wheel and axle is used for many purposes & they are still in business after all their competition has dropped by the wayside. Worksman started in the 1890's and built rugged. They are way overbuilt, including axle strength, because people abuse their tools and then want to file litigation.
My "small axles" are not a concern to me on my Gator, but then this is your build & your the one who has to decide what both what the question is & it's answer. Have fun! Rick C.