Tom and Norma,
I don't know how relevant it is, but some time ago, I and another member, widespreadpizza (Marc), conducted a series of experiments in which we used no commercial yeast whatsoever, and relied only on what we believed to be natural yeast from the flour and surroundings. The dough is all cases was fermented at room temperature, both in the hot summer months and also in winter. You can see Marc's results with his dough starting at Reply 77 at
http://www.pizzamaking.com/forum/index.php?topic=7225.msg78742#msg78742. The dough shown in Marc's photos had no commercial yeast whatsoever. Marc's finished pizza is shown in Reply 82 at
http://www.pizzamaking.com/forum/index.php?topic=7225.msg78756#msg78756.
I conducted my own tests using no commercial yeast and described the results starting at Reply 78 at
http://www.pizzamaking.com/forum/index.php?topic=7225.msg78743#msg78743. Photos of my finished pizzas that were based on doughs with no commercial yeast, along with the formulations I used, can be seen at Reply 84 at
http://www.pizzamaking.com/forum/index.php?topic=7225.msg78779#msg78779, Reply 121 at
http://www.pizzamaking.com/forum/index.php?topic=7225.msg79287#msg79287, Reply 124 at
http://www.pizzamaking.com/forum/index.php?topic=7225.msg89301#msg89301 and Reply 128 at
http://www.pizzamaking.com/forum/index.php?topic=7225.msg92094#msg92094.
All along, Marc and I believed that our doughs were fermenting and rising due to that action of wild yeast. It wasn't until another member, in another thread, mentioned that it was more likely that it was a species of bacteria that was causing the fermentation and dough rise. I remembered the member's name (cornicione54) but since he had requested that his account be closed, he could no longer be found in the forum's membership rolls to be able to search his posts, even though the posts still existed. So, I did a Google search to see if I could find the name of the bacterium that cornicione54 had mentioned. I found it at page 2 of the document at
http://web.oranim.ac.il/courses/microbiology/Bacterial%20Fermentation%20Nature.pdf. The name of the bacterium was leuconostoc and, as shown in that document, it appears that that bacterium can produce carbon dioxide, which is the gas that causes dough to rise, and ethanol. Having found the name of the bacterium, that led me to posts by cornicione54 at Reply 14 at
http://www.pizzamaking.com/forum/index.php?topic=12390.msg117722#msg117722, at Reply 11 at
http://www.pizzamaking.com/forum/index.php?topic=12545.msg119873#msg119873 and at Reply 59 at
http://www.pizzamaking.com/forum/index.php?topic=10237.msg109001;topicseen#msg109001.
I mention the above only because I wonder whether the leuconostoc bacterium might be at play in what you both have been doing, or attempting to do. From what I have read, the leuconostoc bacterium can be negated by using an acid like pineapple juice. But if there is no acid when using something like basil or rosemary, or one of the other materials mentioned earlier in this post, it may still be possible to get a dough to rise, whether natural yeast are or are not present. So, one might be led to believe that a dough is rising because of a natural yeast when maybe it is the leuconostoc bacterium that is doing it.
Peter
EDIT (1/18/21): For the Wayback Machine version of the inoperative oranim article, see
https://web.archive.org/web/20140908223508/http://web.oranim.ac.il/courses/microbiology/Bacterial%20Fermentation%20Nature.pdf