Both your ovens look awesome. It looks like you beveled your dome bricks which is something I wish I could have done. I did all my cutting with a hand held pnuematic grinder and a 4.5 inch masonary blade. I remember those cuts where the dome met with inner arch. That was difficult, trying to keep it from forming a teardrop shape.
So one thing that I wish I had done is pouring a base slab and a second slab for the oven floor. Pouring all that concrete was beyond me at the time, but I wish I had that more stable base and the extra storage underneath would be nice. So those are things for my next build. My block stand sits on a base of pure sand which is several feet deep and tamped. I only hope it does not shift too much over time, but I'm told the sand is much more stable than soil.
It has been a year and it has not moved at all so knock on wood.
I am amazed how that trailer is able to support the weight of your 36 inch oven. That is also the size of my oven. The trailer is very cool.