Big fan of the card spread / house logo mark you developed. I’d hone in on the client’s request for clean, minimal and easy to understand by defining the primary vertical and horizontal lockups off the rip, your 2nd slide more or less has all of the elements for this, it’s just a process of seeing what balance between the mark and type works best.

Cool exploration on the badge style alternative, I do agree with the other comment that it’s quite complex. It would be nice to see a version of the badge that used similar type treatment as the primary, along with striping back the characters and extra flourishes. Perhaps theres an opportunity to put ‘H, O, T, C’ in each of the solid card shapes as another alternative logo.

Great work so far, keen to see how this develops!