From this description it's quite hard to guess what may have happened (do you remember what "couldn't access channels" meant exactly? all gone, weird errors, freezing immediately, etc? when did that start precisely, or in other words did you manage to install and open the HBC?), but in general regardless of the actual cause you may have painted yourself into a corner if you had an usable way to run homebrew and removed it, as simply put yes, the Hackmii Installer is finicky...
Something I never tried would be to simply not use the Hackmii Installer - given the exploit works, per se, and it works while the Wii Menu is running, it might be possible to run a modern wad manager directly from it, which would be able to directly give itself permissions via AHBPROT - but I doubt this would actually work (the Wii Menu has special privileges but that doesn't mean it's crazy enough to have all direct hardware access enabled)
If that crazy idea works you might be able to install the HBC via wad package... or perhaps to run a syscheck instead of the wad manager.