I think, compared to older ovens, it's probably not hugely unique, but I'm relatively certain that if you compared your temps to newer ovens, it would definitely be a freak.
If your oven can consistently pre-heat your stone above 600, that gives you considerable options when choosing a stone. 625 is probably high enough to work with something with as little mass as a 3/4" cordierite kiln shelf or even possibly 1/4" steel plate. If you can consistently pre-heat to 650, then you might be able to even get away with dirt cheap 1/2" quarry tiles. Should you ever buy a new oven, though, it might make your thinner stone obsolete.
I have a 25 year old oven that, if set to 550, cycles between 525 and 600, resulting in a stone that will read 575 after about an hour's pre-heat.
One critical aspect to stone temps that's easy to overlook is that the exterior temp may be different than the interior. I've seen lots of members put the stone close to the broiler (or close to the bottom element), hit 625ish temps and make the assumption that they're baking at 625. In order to see the effects of baking at 625, the stone has to be 625 all the way through. It has to be completely saturated with heat.
I'm not saying this is what's happening with you, but it's good to be aware that IR readings may not be telling the whole story.
I haven't done a whole lot of this type of testing myself, but a good way of determining how much heat has penetrated the stone is to turn off the oven and take temperature readings every 15 minutes. If the stone is fully saturated, the temps should drop more slowly than if the temp has only been ramped up on the surface.