Both factions also have great reverence - cults of personality, really - for their founders. There is potential for a Father, Spirit, Son trinity here with Aleks Kerensky, Jerry Blake, and Nicky Kerensky, respectively. I'm thinking such a religion would start as a deliberate syncretizing of the two cults, but would gradually develop into a more-formal faith, complete with sermons in High Domini.
The culture would likely remain predominately Clan-based, with the Word of Blake slotting mostly into the Technician and Scientist castes. The Manei Domini could form a parallel armed force; they wouldn't have standing in the Hall of Khans, but could supplant the Watch (and they'd be much better at it). The Word could also make up an entirely new caste devoted to religious pursuits. The Cloud Cobras are the most likely to support this.
The military would be fearsome, indeed. Interface cockpits combined with Clan-spec weapons are scary enough in the Parash 3 and Stormcrow III; adding in Blakist cyberwear would be terrifying. For narrative purposes this would have to be limited in some way, so perhaps the concept of the 800 is brought back in a slightly different way: each Clan has ~150ish elite warriors, each with both a Bloodname and an Ascended name. There would be plenty of "lesser" warriors of course, and given the Manei Domini belief that the first sacrifice of flesh must be in battle, these guys are going to be absolutely headstrong. Maybe they'd even prefer light and medium 'Mechs, heavy on speed and guns but light on armor.