Use standard mixer with hook for ten minutes. Don't know exactly what straight dough is but I'm married to a girl if that helps. My flour is Bouncer high gluten with 20% semolina. Been at 52% hydration. Just made a dough ball @ 61% and will see in 5 days how she goes.
The straight dough method calls for mixing and kneading essentially all of the dough ingredients at the same time, even if the ingredients are sequenced into the dough at different times. As I understand it, there would be no use of preferments or autolyse or similar rest periods. Once the dough is kneaded, it is processed further as called for by the recipe.
The reason I asked you whether you were using the straight dough method is because if you were to attempt to use that method with a hydration 0f 72%, even with a high-gluten flour and semolina flour, both of which can take on a lot of water compared with weaker flours, and assuming that you do not use a lot of bench flour, you would most likely end up with a wet and sticky dough that is hard to handle. To get around that problem, you would typically do a lot of stretch and folds on the bench, using minimal bench flour, and allow the dough to rest between the stretch and folds. You would stop the stretch and folds once the dough loses its wetness. Another approach that you could take is to do an extensive knead of the dough using your stand mixer, along the lines, for example, as discussed at https://sites.google.com/site/hollosyt/quickrusticciabattapizza
. In the case of the dough described in that article, the hydration is a bit over 92%, which necessitated the use of parchment paper to be able to make a pizza out of the dough. One of the negatives of this approach is that the dough is kneaded to full gluten development. That is symptomatic of bread dough rather than pizza dough that is typically kneaded to a somewhat underkneaded state. These differences often lead to debates on the forum whether bread dough is the same as pizza dough. Stretch and folds are also creations of bread dough making, so that will also occasionally enter the debates mentioned above.
Another way of improving the handling of a high hydration dough is to sift the flour. That breaks up lumps in the flours and separates the flour into grains that allow the dough to hydrate more fully. Since flour is sifted at the miller's facility, there is usually little need to sift flour in the small bags as found in the supermarkets. However, for the large 50-lb bags, the compression (and settling) dynamics of flour in large bags is considerably greater than for small bags of flour. Since you mentioned that you are using Bouncer flour, I assume that you are using a large bag of that flour.
Finally, when using a high hydration dough, if one of your objectives is to get a good oven spring, you will want to use an oven that can deliver a lot of energy to the dough. In Johnny's case, I believe that for some while he was using an old oven that could deliver a temperature of around 300 degrees C (570 degrees F). I believe that he now has a new gas oven although I don't recall what bake temperatures he is able to get out of that oven. There are other ways of improving the degree of oven spring for a high hydration dough, but a high oven temperature is one of the best.