In general, I think the best way to analyze your query regarding modern ovens is not to compare to labels in Shulchan Aruch and cases mentioned there. Rather, I would break down the question like this.
1) YD 108/Reicha/Tanur-Not relevant for many reasons. Our ovens, especially American ones, are large and have ventilation. Additionally, there is no Reicha consecutively, and it is highly unlikely and not recommended to cook Kosher and non-Kosher or meat and dairy simultaneously in the same oven.
3) Mamashus- Pieces of caked on grease could fall from the roof of the oven onto the new food, and if they are edible there would be a problem. However, this can easily be solved by a simple cleaning, and no Kashering is necessary for this concern. More problematic is the possibility that the grates/racks the pans are placed on could have residue on them (Bliyos would not be problematic due to Shtei Kedeiros). A thorough cleaning would solve this issue. A simpler solution is to place a sheet of aluminum foil on the rack and under the pan. This wat, any possible Bliyos will only penetrate the foil, but cannot continue in to the pan due to Shtei Kedairos.
Still, as a general behavior, I cannot recommend using the same oven for Milchigs and Fleishigs, both uncovered. However, minimum precautions are sufficient.
This is just off the cuff, I’m not holding in the Sugya at the moment.