First of all, congrats and welcome to the Sub 2 Hour club.
What I've noticed with my own play is that my performance in combat is absolutely abhorrent, so I've made it a priority to practice the Intro of the game. Your "time-to-deuce", after leaving the Feeding Area and dropping the engine, is 0:05:30. You should be able to scrape 30 seconds or more off your time relatively easily by practicing it and watching the WR video, studying SimpleUnit's strategy. (I.E., Demonspawn are 1 shock, 2 axehits. Shock Battlenuns to spawn adds, then drop engine to kill all in one go)
You can instantly stop sprinting by popping up the Solos menu, so you don't need to swing your axe or have that little delay from coming to a stop.
Bit of the same with fighting the adds @ Metal Queen. Groundpound a group of 4 then give them all a single shock while they're down. Clears it real fast. It's completely up to you when to use your Facemelter, but I've elected to use it in the Queen's third downed-state so that I'm 100% sure I can kill her in one go, and not have to get her downed a second time in one round.
Returning to the Kill Master with 00:36 on the clock is a bit ehh. Try to work on your driving skills there. Just spam nitro, there's no cooldown. My PB on it is either 42/43, but you should definitely try to aim for 00:40 at least.
You seem to take a bit of a roundabout way to get to To The Slaughter (Arming the Razorgirls). I've never timed it myself, but I think heading straight for the light from Bladehenge should be at least a little bit faster.
I'll try to watch a bit more of your recording later. Definitely keep at it, and good luck on your future runs!