Enduser, from what I've seen, very few people have ever pushed the limits on low thermal mass ovens, either mortared or mortarless. If you are, for the sake of portability, going with less thermal mass, you're entering into somewhat uncharted territory.
I see, from your profile, that your favorite pizza is wood fired NY. If you are, indeed, looking for NY bake times, that might give you a little more flexibility when it comes to materials, but, at the same time, you will loose a bit of flexibility when it comes to size. A huge part of what makes an Apizza Scholls pizza great is it's size- 18". Smaller NY style pizzas just aren't as good. To accommodate an 18" pizza, you'll need a pretty big hearth- maybe 22" deep x 38" wide.
I don't think I've ever seen anyone do this, but with proper insulation, firebrick splits (half thickness bricks) should work for the hearth. For the ceiling, you could probably get away with even less thermal mass. I don't have a lot of faith in oil drum thickness steel, but, again, with good insulation, you might be able to get away with 1/4" or maybe even 1/8" steel plate. If you really want to approach the thermal mass aggressively, you might be able to get away with cordierite kiln shelves for the hearth. Generally speaking, the smaller the shelf, the more thermally durable it is, so I would shoot for a few smaller shelves rather than a huge one- maybe 6 14 x 16 x 1/2" shelves arranged in 2 rows of three.
This is also completely uncharted territory, but I think you might be able to get away with 1/8" steel plate on the walls, perhaps supported by angle iron.
At the end of the day, the hearth, walls and ceiling will most likely be the easiest part of the project. Insulating, weatherproofing and venting it are going to get tricky.
Board insulation is sturdy, portable and light, but is costly. I've never cast perlcrete, but I get the feeling it may not be all that durable riding around in the back of a car. Blanket insulation is great for keeping the heat in, but I don't think it's something you want to handle frequently.
Board insulation might be waterproof, but it will still be sitting flat, so, for drainage, you'll need some sort of structure on top of it. You could probably put together a plywood structure that will travel flat.
Ideally, you want a chimney with some thermal mass, but you might be able to get away with well insulated steel.