The entire discussion hinges on certain assumptions, the primary ones being that steam or condensation is an issue in this case and that steel/aluminum is boleya. In addition to this, the discussion of steam being an issue is in an enclosed oven (both vented and non-vented models) which seems would not be an issue in this case, being that it is fully open (cf. `Arokh HaShulhan 92:55).
While it is true that the Rama in the Shulhan `Arukh (92:8) is mahmir regarding steam (zeyah) relying on a teshuvah of the Rosh (20:26) [who quotes a Mishnah in Masekheth Makhshirim (2:2)], the fact is that the sugya in the Gemara which discusses the whole issue of an oven (b.Pesahim 76b, see also y.Terumoth 10:2) and kosher and non-kosher foods being cooked in it does not even mention zeyah as an issue, concludes that reyha (aroma) is law miltha (not a halakhic issue), and is only discussing kosher and non-kosher meat simultaneously.
Also, as is common in Ashkenazi pesiqath halakhah, there is an equivocation between the laws of hekhsher/tumah wa-ttaharah with the laws of kashruth. While there is some overlap, they are definitely separate, as anyone who reads Hilkhoth Tumath Okhalin and Hilkhoth Ma'akhaloth Asuroth will be able to easily ascertain. Thus, the reason why Rosh has to bring a proof from m.Makhshirim regarding the condensation in a bath house being tamei is because the whole idea of steam is not considered an issue within the scope of kashruth until the equivocation of the two areas of halakhah at a much later time in Jewish history. Hazal makes no such claim in the sources which they left to us.
As for the types of materials which are subject to beli`uth (absorption), the Gemara is discussing klei heres (porous pottery/adobe) and not metal at all. Many today hold that metal (stainless steel/aluminum) is not boleya and thus not subject to these laws anyhow, except by those who feel it is necessary to be mahmir.
All this being said, I would say that le'aniyuth da`ati that all that needs to be done to use this pizza oven is a thorough cleaning to remove outer food residue (particles, grease, oil, etc.), and perhaps a lining of the pan where the pizza actually sits with foil as a caution.
I hope that this helps. Kol tuv.