Too bad the tech didn't seem to know much.
I suspect that it's not a true temperature you're seeing. When the floor is out, the oven temperature probe is exposed to the IR from the flame... is that how you're measuring the temperature when it "shoots up"? You could try checking it with the floor removed and an oven thermometer on a sheet pan, with another sheet pan on the shelf below to shield the top pan from the direct flame.
The fact that it takes so long to reach low temperature makes me suspect fuel, whether it's the wrong orifice or a blockage in the gas line or valve. It's hard to tell from the video, was the broiler flame bigger/stronger than the oven flame with the floor out?
I thought that you could be right with this, that maybe the temp I was seeing without the floor was not the real temp. So I did something similar to what you asked. I put my cordierite stone in the top shelf but I didn't put anything under it, my mistake, I guess I should have put something under it to block the flame but it was the top shelf and the flame is a bit far.
I recorded a small video so you could see, i'll post it here, the temps of my stone after about 30 to 40 minutes were pretty high, I reached 575 Fahrenheit on my stone using the IR thermometer. I think it even went a bit higher when I turned on the broiler for a few minutes (this shuts off the bottom burner)
So I don't know what to think, all I know is that I could have baked an awesome pizza on that stone if I wanted to, I think my broiler is old school, obviously gas, so I am not even sure it shuts off with the oven door closed. Still, I've read it's better to make pizzas with the door open?
What do you guys think? Should I just let my wife keep using it as always (she wants this, doesn't want me messing with her area... you know how that is) and whenever I want a good NY style pizza, just remove the bottom, heat my steel/stone and do what I did in my testing right now?
I've been living in this house with that oven for over 7 years and I've never seen it reach those temps, if you told me that oven was capable of heating a thick cordierite stone like the one I am using t 575 Fahrenheit in 40 minutes or less I would have laughed in your face. So I am in a bit of a shock.
Here is the video link. Wow I just realized I went vertical with the video... I never do this, I am sorry, I was taking pictures and completely forgot to turn it.https://www.dropbox.com/sh/7ogf0k6cfgzsmd9/AABtVk_J_eP9hjBuOFDc65_4a?dl=0
And some pictures as well