I'm not familiar with High Alumina cement but I have been curious about adding fine aluminum powder to a cement/perlite mix. Autoclaved aerated concrete is made similar to this by adding aluminum powder to a cement and sand slurry. The aluminum reacts with the cement and causes bubbles to form. After it sets up it is shaped (it's soft at this point) and then cured in an autoclave. My feeling is if you replaced the sand with perlite it may make a good core. My concern is that aluminum burns if hot enough and is it safe, with the now reacted form of aluminum, to not cause a problem.
My choice would be castable refractory. This is different from high alumina cement, the castable has grog in it, commonly made of ground fire bricks and some other additions. The lower part of the riser in a Batch Box Rocket in particular is thermodynamically challenged to put it mildly, better use good quality refractory. Harbison-Walker is a supplier of this type of high quality stuff.
I could mention a brand which is common in the Netherlands but that's almost certainly not what you want to know. But a search resulted in one refractory cement at Amazon's which is certainly a good choice. Brands are Red Devil or Rutland, sometimes in tubes. Insulation could be done with clay stabilized perlite like the guy with the rocket fired boiler did.