Since the King Arthur flours are widely available in the U.S., I can only conclude that you live outside of the U.S. Also, the specs you posted suggest that the flours you listed may not be malted, as by the addition of amylase enzyme in some form, such as dry diastatic barley malt.
For comparison purposes, the specs for the King Arthur flours are given at http://www.kingarthurflour.com/professional/specifications-conventional-bakery-flour.html
. Of the flours listed there, the Sir Lancelot and Special flours woul be the best choices for a Papa John's clone dough. Another flour that is comparable in some respects to the King Arthur Special bread flour is the General Mills Better for Bread (Harvest King) bread flour. The specs for that flour are given at http://www.gmflour.com/gmflour/Flour_SpecSheet/HarvestKing53722.doc
Comparing the abovereferenced specs with the specs you provided, one of the major differences is the falling number. The falling number is an indication of the degree of amylase enzyme activity. A high falling number, as in the specs you provided, suggests low amylase enzyme activity; a low falling number suggest a higher degree of amylase enzyme activity. For a discussion of falling numbers, see the following excerpt from http://www.cooknaturally.com/detailed/detailed.html
:The falling number test determines the alpha-amylase activity of a flour sample. The test entails heating measured amounts of water and flour in a special tube. The tube is placed in a boiling water bath and stirred with a plunger until the sample is gelatinized. Then the plunger is placed on the surface of the sample, and the time that it takes the plunger to sink to the bottom of the tube is recorded. Depending on the alpha-amylase activity, the degradation of the starch paste will vary. The higher the alpha-amylase activity, the lower the number, and vice versa. Typically the falling number has to be adjusted through the addition of diastatic malt, or fungal amylase. Such adjustments are usually done at the mill, along with the enrichment package. Our organic flours are un-malted, so they have high falling numbers, generally in excess of four hundred. Malted bread flours have falling numbers of: 250-290. Generally the baker will find that fermentation progresses more rapidly as falling numbers become lower.
I am not a flour expert, but based on the information you provided, I would be inclined to use either flour #1 or flour #2. Also, to get closer to the King Arthur flours, I would add some dry diastatic barley malt in order to increase the amylase enzyme activity. That is what is done for most flours milled in the U.S. To start, I would use around 0.5% diastatic barley malt as a percent of flour weight. Since diastatic malt works on damaged starch, I would also be inclined to run the flour through my food processor to hopefully increase the degree of damaged starch. Even if I did not have any diastatic malt available to me, I think I would still run the flour through my food processor. I don't know where you flour comes from, but many flours outside of the U.S. have less damaged starch than those milled from wheat in the U.S. In your case, you might even run two tests, one using diastatic malt and one without the diastatic malt.
For a much more thorough and comprehensive discussion of the use of malt in flours, see the article at http://www.pizzamaking.com/forum/index.php/topic,8308.0.html
. In reading this article, you should keep in mind that nondiastatic malts are not the same as diastatic malts.
Please let us know how things work out.