Morning Jim;
First let me say that you did a good job in constructing the kiln you built, the general workmanship is very good. Second, allow me to say that while the properties of firebrick have not changed since I was involved in these matters the technology of refractory materials, casting medias and building materials, etc., has; and I am simply not up to date on them so do not know what is out there for making a device such as yours. I will phone my son this evening and see if he can bring us up to speed on those things, question him on what the best options are these days. I will get back with you when I have communicated with him.
At this point I will venture that you will likely end up using mostly soft brick for the little kiln, and some sort of material covering the outside. I looked at the temp controller unit you linked to - I cannot advise you on it as I am not familiar with it although it looks to work within the range of temperatures you will be using. How well it works, its lifespan, I do not know. By the way, don't make a habit of looking directly into a fired up kiln, use eye protection such as a welders glass or goggles. Lots of UV and other eye harmful light coming out of that interior.
To sum up: I will talk with my son and get back with you. Hopefully he will have some up to date information for you.
dave
ADD: Mortar - When I was building pottery kilns I avoided mortar like the plague, over time it tends to crumble and bit by bit fall into the interior of the kiln. No refractory mortar, in my day, would withstand the thermal expansion and contraction of repeated firings. We, of course, are talking of much smaller construction so I have no experience of that and do not know how a bit of mortar would function at the scale we are talking.